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Volumn 70, Issue , 2010, Pages 1-238

Bifurcations in piecewise-smooth continuous systems

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EID: 85122400748     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1142/7612     Document Type: Book
Times cited : (109)

References (294)
  • 1
    • 0012848717 scopus 로고    scopus 로고
    • Dynamical simulation of rigid bodies: Modelling of frictional contact
    • in B. Brogliato (ed.), Springer-Verlag, New York
    • Abadie, M. (2000). Dynamical simulation of rigid bodies: Modelling of frictional contact. in B. Brogliato (ed.), Impacts in Mechanical Systems: Analysis and Modelling. (Springer-Verlag, New York).
    • (2000) Impacts in Mechanical Systems: Analysis and Modelling
    • Abadie, M.1
  • 2
    • 17444410970 scopus 로고    scopus 로고
    • Global bifurcations of closed invariant curves in two-dimensional maps: A computer assisted study
    • Agliari, A., Bischi, G., Dieci, R. and Gardini, L. (2005). Global bifurcations of closed invariant curves in two-dimensional maps: A computer assisted study. Int. J. Bifurcation Chaos 15, 4, pp. 1285-1328.
    • (2005) Int. J. Bifurcation Chaos , vol.15 , Issue.4 , pp. 1285-1328
    • Agliari, A.1    Bischi, G.2    Dieci, R.3    Gardini, L.4
  • 3
    • 0001918755 scopus 로고
    • On the stability of periodic motions
    • Aizerman, M. and Gantmakher, F. (1958). On the stability of periodic motions. J. Appl. Math. Mech. 22, 6, pp. 750-758.
    • (1958) J. Appl. Math. Mech. , vol.22 , Issue.6 , pp. 750-758
    • Aizerman, M.1    Gantmakher, F.2
  • 5
    • 0035419722 scopus 로고    scopus 로고
    • Robust chaos in smooth unimodal maps
    • Andrecut, M. and Ali, M. (2001). Robust chaos in smooth unimodal maps. Phys. Rev. E 64, 2, p. 025203.
    • (2001) Phys. Rev. E , vol.64 , Issue.2 , pp. 025203
    • Andrecut, M.1    Ali, M.2
  • 7
    • 54749141192 scopus 로고    scopus 로고
    • Two-parameter discontinuity-induced bifurcation curves in a ZAD-strategy-controlled DC-DC buck converter
    • Angulo, F., Olivar, G. and di Bernardo, M. (2008). Two-parameter discontinuity-induced bifurcation curves in a ZAD-strategy-controlled DC-DC buck converter. IEEE Trans. Circuits Systems I Fund. Theory Appl. 55, 8, pp. 2392-2401.
    • (2008) IEEE Trans. Circuits Systems I Fund. Theory Appl. , vol.55 , Issue.8 , pp. 2392-2401
    • Angulo, F.1    Olivar, G.2    di Bernardo, M.3
  • 8
    • 32044439614 scopus 로고    scopus 로고
    • Bifurcation and chaos of a simple walking model driven by a rhythmic signal
    • Aoi, S. and Tsuchiya, K. (2006). Bifurcation and chaos of a simple walking model driven by a rhythmic signal. Int. J. Non-Linear Mech. 41, pp. 438-446.
    • (2006) Int. J. Non-Linear Mech , vol.41 , pp. 438-446
    • Aoi, S.1    Tsuchiya, K.2
  • 10
    • 0000009552 scopus 로고
    • Bifurcations from an invariant circle for two-parameter families of maps of the plane: A computer-assisted study
    • Aronson, D., Chory, M., Hall, G. and McGehee, R. (1982). Bifurcations from an invariant circle for two-parameter families of maps of the plane: A computer-assisted study. Comm. Math. Phys. 83, pp. 303-354.
    • (1982) Comm. Math. Phys , vol.83 , pp. 303-354
    • Aronson, D.1    Chory, M.2    Hall, G.3    McGehee, R.4
  • 12
    • 29844456166 scopus 로고    scopus 로고
    • On special types of two- and three-parametric bifurcations in piecewise-smooth dynamical systems
    • Avrutin, V. and Schanz, M. (2005a). On special types of two- and three-parametric bifurcations in piecewise-smooth dynamical systems. WSEAS Trans. Math. 4, 3, pp. 224-230.
    • (2005) WSEAS Trans. Math. , vol.4 , Issue.3 , pp. 224-230
    • Avrutin, V.1    Schanz, M.2
  • 13
    • 22144444576 scopus 로고    scopus 로고
    • Period-doubling scenario without flip bifurcations in a one-dimensional map
    • Avrutin, V. and Schanz, M. (2005b). Period-doubling scenario without flip bifurcations in a one-dimensional map. Int. J. Bifurcation Chaos 15, 4, pp. 1267-1284.
    • (2005) Int. J. Bifurcation Chaos , vol.15 , Issue.4 , pp. 1267-1284
    • Avrutin, V.1    Schanz, M.2
  • 14
    • 43049088133 scopus 로고    scopus 로고
    • On the fully developed bandcount adding scenario
    • Avrutin, V. and Schanz, M. (2008). On the fully developed bandcount adding scenario. Nonlinearity 21, pp. 1077-1103.
    • (2008) Nonlinearity , vol.21 , pp. 1077-1103
    • Avrutin, V.1    Schanz, M.2
  • 15
    • 33748978617 scopus 로고    scopus 로고
    • Multi-parametric bifurcations in a piecewise-linear discontinuous map
    • Avrutin, V., Schanz, M. and Banerjee, S. (2006). Multi-parametric bifurcations in a piecewise-linear discontinuous map. Nonlinearity 19, pp. 1875-1906.
    • (2006) Nonlinearity , vol.19 , pp. 1875-1906
    • Avrutin, V.1    Schanz, M.2    Banerjee, S.3
  • 16
    • 34547261015 scopus 로고    scopus 로고
    • Codimension-three bifurcations: Explanation of the complex one-, two-, and three-dimensional bifurcation structures in nonsmooth maps
    • Avrutin, V., Schanz, M. and Banerjee, S. (2007). Codimension-three bifurcations: Explanation of the complex one-, two-, and three-dimensional bifurcation structures in nonsmooth maps. Phys. Rev. E. 75, p. 066205.
    • (2007) Phys. Rev. E. , vol.75 , pp. 066205
    • Avrutin, V.1    Schanz, M.2    Banerjee, S.3
  • 17
    • 14844302647 scopus 로고    scopus 로고
    • Investigation of triple pendulum with impacts using fundamental solution matrices
    • Awrejcewicz, J., Kudra, G. and Lamarque, C. (2004). Investigation of triple pendulum with impacts using fundamental solution matrices. Int. J. Bifurcation Chaos 14, 12, pp. 4191-4213.
    • (2004) Int. J. Bifurcation Chaos , vol.14 , Issue.12 , pp. 4191-4213
    • Awrejcewicz, J.1    Kudra, G.2    Lamarque, C.3
  • 21
    • 0000780796 scopus 로고    scopus 로고
    • Border collision bifurcations in two-dimensional piecewise smooth maps
    • Banerjee, S. and Grebogi, C. (1999). Border collision bifurcations in two-dimensional piecewise smooth maps. Phys. Rev. E 59, 4, pp. 4052-4061.
    • (1999) Phys. Rev. E , vol.59 , Issue.4 , pp. 4052-4061
    • Banerjee, S.1    Grebogi, C.2
  • 22
    • 0034156883 scopus 로고    scopus 로고
    • Bifurcations in one-dimensional piecewise smooth maps - Theory and applications in switching circuits
    • Banerjee, S., Karthik, M., Yuan, G. and Yorke, J. (2000a). Bifurcations in one-dimensional piecewise smooth maps - Theory and applications in switching circuits. IEEE Trans. Circuits Systems I Fund. Theory Appl. 47, 3, pp. 389-394.
    • (2000) IEEE Trans. Circuits Systems I Fund. Theory Appl. , vol.47 , Issue.3 , pp. 389-394
    • Banerjee, S.1    Karthik, M.2    Yuan, G.3    Yorke, J.4
  • 23
    • 0033698914 scopus 로고    scopus 로고
    • Bifurcations in two-dimensional piecewise smooth maps - Theory and applications in switching circuits
    • Banerjee, S., Ranjan, P. and Grebogi, C. (2000b). Bifurcations in two-dimensional piecewise smooth maps - Theory and applications in switching circuits. IEEE Trans. Circuits Systems I Fund. Theory Appl. 47, 5, pp. 633-643.
    • (2000) IEEE Trans. Circuits Systems I Fund. Theory Appl. , vol.47 , Issue.5 , pp. 633-643
    • Banerjee, S.1    Ranjan, P.2    Grebogi, C.3
  • 27
    • 33749479699 scopus 로고    scopus 로고
    • Periodic solutions and their bifurcations in a non-smooth second-order delay differential equation
    • Barton, D., Krauskopf, B. and Wilson, R. (2006). Periodic solutions and their bifurcations in a non-smooth second-order delay differential equation. Dyn. Syst. 21, 3, pp. 289-311.
    • (2006) Dyn. Syst. , vol.21 , Issue.3 , pp. 289-311
    • Barton, D.1    Krauskopf, B.2    Wilson, R.3
  • 28
    • 34748876801 scopus 로고    scopus 로고
    • Numerical bifurcation analysis of a friction-driven vibro-impact system
    • Batako, A., Lalor, M. and Piiroinen, P. (2007). Numerical bifurcation analysis of a friction-driven vibro-impact system. J. Sound Vib. 308, pp. 392-404.
    • (2007) J. Sound Vib , vol.308 , pp. 392-404
    • Batako, A.1    Lalor, M.2    Piiroinen, P.3
  • 29
    • 0034383432 scopus 로고    scopus 로고
    • Symbolic dynamics in nondifferentiable system originating in R-L-diode driven circuit
    • Belghith, S. (2000). Symbolic dynamics in nondifferentiable system originating in R-L-diode driven circuit. Disc. Cont. Dyn. Sys. 6, 2, pp. 275-292.
    • (2000) Disc. Cont. Dyn. Sys. , vol.6 , Issue.2 , pp. 275-292
    • Belghith, S.1
  • 30
    • 0034291822 scopus 로고    scopus 로고
    • Observability and controllability of piecewise affine and hybrid systems
    • Bemporad, A., Ferrari-Trecate, G. and Morari, M. (2000). Observability and controllability of piecewise affine and hybrid systems. IEEE Trans. Automat. Contr. 45, 10, pp. 1864-1876.
    • (2000) IEEE Trans. Automat. Contr. , vol.45 , Issue.10 , pp. 1864-1876
    • Bemporad, A.1    Ferrari-Trecate, G.2    Morari, M.3
  • 31
    • 0033097938 scopus 로고    scopus 로고
    • Control of systems integrating logic, dynamics, and constraints
    • Bemporad, A. and Morari, M. (1999). Control of systems integrating logic, dynamics, and constraints. Automatica 35, pp. 407-427.
    • (1999) Automatica , vol.35 , pp. 407-427
    • Bemporad, A.1    Morari, M.2
  • 32
    • 0038333576 scopus 로고    scopus 로고
    • Two-dimensional bifurcation diagrams. Background pattern of fundamental DC-DC converters with PWM control
    • Benadero, L., El Aroundi, A., Olivar, G., Toribio, E. and Gómez, E. (2003). Two-dimensional bifurcation diagrams. Background pattern of fundamental DC-DC converters with PWM control. Int. J. Bifurcation Chaos 13, 2, pp. 427-451.
    • (2003) Int. J. Bifurcation Chaos , vol.13 , Issue.2 , pp. 427-451
    • Benadero, L.1    El Aroundi, A.2    Olivar, G.3    Toribio, E.4    Gómez, E.5
  • 33
    • 0004761246 scopus 로고
    • Oxford University Press, New York
    • Berberian, S. (1992). Linear Algebra. (Oxford University Press, New York).
    • (1992) Linear Algebra
    • Berberian, S.1
  • 34
    • 33750043496 scopus 로고    scopus 로고
    • Structurally stable PWL approximation of nonlinear dynamical systems admitting limit cycles: An example
    • Bergami, M., Bizzarri, F., Carlevaro, A. and Storace, M. (2006). Structurally stable PWL approximation of nonlinear dynamical systems admitting limit cycles: An example. IEICE Trans. Fund. E89-A, 10, pp. 2759-2766.
    • (2006) IEICE Trans. Fund. E89-A, , vol.10 , pp. 2759-2766
    • Bergami, M.1    Bizzarri, F.2    Carlevaro, A.3    Storace, M.4
  • 36
    • 49149128642 scopus 로고    scopus 로고
    • Periodicity hub and nested spirals in the phase diagram of a simple resistive circuit
    • Bonatto, C. and Gallas, J. (2008). Periodicity hub and nested spirals in the phase diagram of a simple resistive circuit. Phys. Rev. Lett. 101, 5, p. 054101.
    • (2008) Phys. Rev. Lett. , vol.101 , Issue.5 , pp. 054101
    • Bonatto, C.1    Gallas, J.2
  • 37
    • 33646027172 scopus 로고
    • Bifurcations of circle maps: Arnol'd tongues, bistability and rotation intervals
    • Boyland, P. (1986). Bifurcations of circle maps: Arnol'd tongues, bistability and rotation intervals. Comm. Math. Phys. 106, 3, pp. 353-381.
    • (1986) Comm. Math. Phys. , vol.106 , Issue.3 , pp. 353-381
    • Boyland, P.1
  • 38
    • 0032047505 scopus 로고    scopus 로고
    • Multiple Lyapunov functions and other analysis tools for switched and hybrid systems
    • Branicky, M. (1998). Multiple Lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Trans. Automat. Contr. 43, 4, pp. 475-482.
    • (1998) IEEE Trans. Automat. Contr. , vol.43 , Issue.4 , pp. 475-482
    • Branicky, M.1
  • 39
    • 34748826913 scopus 로고    scopus 로고
    • Mean-field analysis of an inductive reasoning game: Application to influenza
    • Breban, R., Vardavas, R. and Blower, S. (2007). Mean-field analysis of an inductive reasoning game: Application to influenza. Phys. Rev. E 76, p. 031127.
    • (2007) Phys. Rev. E , vol.76 , pp. 031127
    • Breban, R.1    Vardavas, R.2    Blower, S.3
  • 41
    • 33747055006 scopus 로고    scopus 로고
    • Corner bifurcations in non-smoothly forced impact oscillators
    • Budd, C. and Piiroinen, P. (2006). Corner bifurcations in non-smoothly forced impact oscillators. Phys. D 220, pp. 127-145.
    • (2006) Phys. D , vol.220 , pp. 127-145
    • Budd, C.1    Piiroinen, P.2
  • 42
    • 33749598028 scopus 로고    scopus 로고
    • A singular approach to discontinuous vector fields on the plane
    • Buzzi, C., da Silva, P. and Teixeira, M. (2006). A singular approach to discontinuous vector fields on the plane. J. Differential Equations 231, pp. 633-655.
    • (2006) J. Differential Equations , vol.231 , pp. 633-655
    • Buzzi, C.1    da Silva, P.2    Teixeira, M.3
  • 43
    • 33745737184 scopus 로고    scopus 로고
    • Chaotic dynamics in credit constrained emerging economies
    • Caballé, J., Jarque, X. and Michetti, E. (2006). Chaotic dynamics in credit constrained emerging economies. J. Econ. Dyn. Control 30, pp. 1261- 1275.
    • (2006) J. Econ. Dyn. Control , vol.30 , pp. 1261- 1275
    • Caballé, J.1    Jarque, X.2    Michetti, E.3
  • 46
    • 25844515841 scopus 로고    scopus 로고
    • Bifurcation of invariant cones in piecewise linear homogeneous systems
    • Carmona, V., Freire, E., Ponce, E. and Torres, F. (2005b). Bifurcation of invariant cones in piecewise linear homogeneous systems. Int. J. Bifurcation Chaos 15, 8, pp. 2469-2484.
    • (2005) Int. J. Bifurcation Chaos , vol.15 , Issue.8 , pp. 2469-2484
    • Carmona, V.1    Freire, E.2    Ponce, E.3    Torres, F.4
  • 47
    • 33845767382 scopus 로고    scopus 로고
    • The continuous matching of two stable linear systems can be unstable
    • Carmona, V., Freire, E., Ponce, E. and Torres, F. (2006). The continuous matching of two stable linear systems can be unstable, Disc. Cont. Dyn. Sys. 16, 3, pp. 689-703.
    • (2006) Disc. Cont. Dyn. Sys. , vol.16 , Issue.3 , pp. 689-703
    • Carmona, V.1    Freire, E.2    Ponce, E.3    Torres, F.4
  • 48
    • 29244452623 scopus 로고    scopus 로고
    • Piecewise-linear models of genetic regulatory networks: Equilibria and their stability
    • Casey, R., de Jong, H. and Gouzé, J. (2006). Piecewise-linear models of genetic regulatory networks: Equilibria and their stability. J. Math. Biol. 52, pp. 27-56.
    • (2006) J. Math. Biol , vol.52 , pp. 27-56
    • Casey, R.1    de Jong, H.2    Gouzé, J.3
  • 49
    • 33750164513 scopus 로고    scopus 로고
    • Experimental evidence of non-standard bifurcations in non-smooth oscillator dynamics
    • Casini, P., Giannini, O. and Vestroni, F. (2006). Experimental evidence of non-standard bifurcations in non-smooth oscillator dynamics. Nonlinear Dyn. 46, 3, pp. 259-272.
    • (2006) Nonlinear Dyn. , vol.46 , Issue.3 , pp. 259-272
    • Casini, P.1    Giannini, O.2    Vestroni, F.3
  • 50
    • 13844276983 scopus 로고    scopus 로고
    • Piecewise two-dimensional maps and applications to cellular neural networks
    • Chang, H. and Juang, J. (2004). Piecewise two-dimensional maps and applications to cellular neural networks. Int. J. Bifurcation Chaos 14, 7, pp. 2223-2228.
    • (2004) Int. J. Bifurcation Chaos , vol.14 , Issue.7 , pp. 2223-2228
    • Chang, H.1    Juang, J.2
  • 52
    • 0000208406 scopus 로고
    • Grazing bifurcations in impact oscillators
    • Chin, W., Ott, E., Nusse, H. and Grebogi, C. (1994). Grazing bifurcations in impact oscillators, Phys. Rev. E 50, 6, pp. 4427-4450.
    • (1994) Phys. Rev. E , vol.50 , Issue.6 , pp. 4427-4450
    • Chin, W.1    Ott, E.2    Nusse, H.3    Grebogi, C.4
  • 53
    • 0028465976 scopus 로고
    • Chua's circuit 10 years later
    • Chua, L. (1994). Chua's circuit 10 years later. Internat. J. Circuit Theory Appl. 22, 4, pp. 279-305.
    • (1994) Internat. J. Circuit Theory Appl. , vol.22 , Issue.4 , pp. 279-305
    • Chua, L.1
  • 54
    • 0023866658 scopus 로고
    • Canonical piecewise-linear representation
    • Chua, L. and Deng, A. (1988). Canonical piecewise-linear representation. IEEE Trans. Circuits Systems 35, 1, pp. 101-111.
    • (1988) IEEE Trans. Circuits Systems , vol.35 , Issue.1 , pp. 101-111
    • Chua, L.1    Deng, A.2
  • 55
    • 0025461076 scopus 로고
    • Canonical realization of Chua's circuit family
    • Chua, L. and Lin, G. (1990). Canonical realization of Chua's circuit family. IEEE Trans. Circuits Systems 37, 7, pp. 885-902.
    • (1990) IEEE Trans. Circuits Systems , vol.37 , Issue.7 , pp. 885-902
    • Chua, L.1    Lin, G.2
  • 56
    • 0026153216 scopus 로고
    • Intermittency in a piecewise-linear circuit
    • Chua, L. and Lin, G. (1991). Intermittency in a piecewise-linear circuit. IEEE Trans. Circuits Systems 38, 5, pp. 510-520.
    • (1991) IEEE Trans. Circuits Systems , vol.38 , Issue.5 , pp. 510-520
    • Chua, L.1    Lin, G.2
  • 57
    • 85122385253 scopus 로고    scopus 로고
    • Discontinuity induced bifurcations of non-hyperbolic cycles in nonsmooth systems
    • Colombo, A. and Dercole, F. (unpublished). Discontinuity induced bifurcations of non-hyperbolic cycles in nonsmooth systems. Submitted to: SIAM J. Appl. Dyn. Sys.
    • Submitted to: SIAM J. Appl. Dyn. Sys.
    • Colombo, A.1    Dercole, F.2
  • 58
    • 0001501979 scopus 로고
    • A numerical study of an impact oscillator with the addition of dry friction
    • Cone, K. and Zadoks, R. (1995). A numerical study of an impact oscillator with the addition of dry friction. J. Sound Vib. 188, 5, pp. 659-683.
    • (1995) J. Sound Vib. , vol.188 , Issue.5 , pp. 659-683
    • Cone, K.1    Zadoks, R.2
  • 59
    • 0034257995 scopus 로고    scopus 로고
    • Period-adding bifurcations and chaos in a periodically stimulated excitable neural relaxation oscillator
    • Coombes, S. and Osbaldestin, A. (2000). Period-adding bifurcations and chaos in a periodically stimulated excitable neural relaxation oscillator. Phys. Rev. E 62, 3, pp. 4057-4066.
    • (2000) Phys. Rev. E , vol.62 , Issue.3 , pp. 4057-4066
    • Coombes, S.1    Osbaldestin, A.2
  • 61
    • 33745146535 scopus 로고    scopus 로고
    • On the periodic response of a harmonically excited dry friction oscillator
    • Csernák, G. and Stépán, G. (2006). On the periodic response of a harmonically excited dry friction oscillator. J. Sound Vibrat. 295, pp. 649-658.
    • (2006) J. Sound Vibrat , vol.295 , pp. 649-658
    • Csernák, G.1    Stépán, G.2
  • 62
    • 0042378913 scopus 로고    scopus 로고
    • Sliding bifurcations of equi-libria in planar variable structure systems
    • Cunha, F., Pagano, D. and Moreno, U. (2003). Sliding bifurcations of equi-libria in planar variable structure systems. IEEE Trans. Circuits Systems I Fund. Theory Appl. 50, 8, pp. 1129-1134.
    • (2003) IEEE Trans. Circuits Systems I Fund. Theory Appl. , vol.50 , Issue.8 , pp. 1129-1134
    • Cunha, F.1    Pagano, D.2    Moreno, U.3
  • 63
    • 34547986819 scopus 로고    scopus 로고
    • Slow-scale instability of single-stage power-factor-correction power supplies
    • Dai, D., Li, S., Ma, X. and Tse, C. (2007). Slow-scale instability of single-stage power-factor-correction power supplies. IEEE Trans. Circuits Systems I Fund. Theory Appl. 54, 8, pp. 1724-1735.
    • (2007) IEEE Trans. Circuits Systems I Fund. Theory Appl. , vol.54 , Issue.8 , pp. 1724-1735
    • Dai, D.1    Li, S.2    Ma, X.3    Tse, C.4
  • 64
    • 0346688041 scopus 로고    scopus 로고
    • On the origin and bifurcations of stick-slip oscillations
    • Dankowicz, H. and Nordmark, A. (2000). On the origin and bifurcations of stick-slip oscillations. Phys. D 136, pp. 280-302.
    • (2000) Phys. D , vol.136 , pp. 280-302
    • Dankowicz, H.1    Nordmark, A.2
  • 65
    • 0036939763 scopus 로고    scopus 로고
    • Exploiting discontinuities for stabilization of recurrent motions
    • Dankowicz, H. and Piiroinen, P. (2002). Exploiting discontinuities for stabilization of recurrent motions. Dynamical Systems 17, 4, pp. 317-342.
    • (2002) Dynamical Systems , vol.17 , Issue.4 , pp. 317-342
    • Dankowicz, H.1    Piiroinen, P.2
  • 68
    • 24144495590 scopus 로고    scopus 로고
    • Border collision bifurcations in the evolution of mutu-alistic interactions
    • Dercole, F. (2005). Border collision bifurcations in the evolution of mutu-alistic interactions. Int. J. Bifurcation Chaos 15, 7, pp. 2179-2190.
    • (2005) Int. J. Bifurcation Chaos , vol.15 , Issue.7 , pp. 2179-2190
    • Dercole, F.1
  • 69
    • 25644459854 scopus 로고    scopus 로고
    • Detection and continuation of a border collision bifurcation in a forest fire model
    • Dercole, F. and Maggi, S. (2005). Detection and continuation of a border collision bifurcation in a forest fire model. Appl. Math. Comput. 186, pp. 623-635.
    • (2005) Appl. Math. Comput , vol.186 , pp. 623-635
    • Dercole, F.1    Maggi, S.2
  • 70
    • 0041822709 scopus 로고    scopus 로고
    • Grazing, skipping and sliding: Analysis of the non-smooth dynamics of the DC/DC buck converter
    • di Bernardo, M., Budd, C. and Champneys, A. (1998a). Grazing, skipping and sliding: Analysis of the non-smooth dynamics of the DC/DC buck converter. Nonlinearity 11, pp. 859-890.
    • (1998) Nonlinearity , vol.11 , pp. 859-890
    • di Bernardo, M.1    Budd, C.2    Champneys, A.3
  • 71
    • 0035877127 scopus 로고    scopus 로고
    • Corner collision implies border-collision bifurcation
    • di Bernardo, M., Budd, C. and Champneys, A. (2001a). Corner collision implies border-collision bifurcation. Phys. D 154, pp. 171-194.
    • (2001) Phys. D , vol.154 , pp. 171-194
    • di Bernardo, M.1    Budd, C.2    Champneys, A.3
  • 72
    • 0035892830 scopus 로고    scopus 로고
    • Normal form maps for grazing bifurcations in n-dimensional piecewise-smooth dynamical systems
    • di Bernardo, M., Budd, C. and Champneys, A. (2001b). Normal form maps for grazing bifurcations in n-dimensional piecewise-smooth dynamical systems. Phys. D 160, pp. 222-254.
    • (2001) Phys. D , vol.160 , pp. 222-254
    • di Bernardo, M.1    Budd, C.2    Champneys, A.3
  • 74
    • 0033229544 scopus 로고    scopus 로고
    • Local analysis of C-bifurcations in n-dimensional piecewise-smooth dynamical systems
    • di Bernardo, M., Feigin, M., Hogan, S. and Homer, M. (1999). Local analysis of C-bifurcations in n-dimensional piecewise-smooth dynamical systems. Chaos Solitons Fractals 10, 11, pp. 1881-1908.
    • (1999) Chaos Solitons Fractals , vol.10 , Issue.11 , pp. 1881-1908
    • di Bernardo, M.1    Feigin, M.2    Hogan, S.3    Homer, M.4
  • 75
    • 0031498483 scopus 로고    scopus 로고
    • Secondary bifurcations and high periodic orbits in voltage controlled buck converter
    • di Bernardo, M., Fossas, E., Olivar, G. and Vasca, F. (1997). Secondary bifurcations and high periodic orbits in voltage controlled buck converter. Int. J. Bifurcation Chaos 7, pp. 2755-2771.
    • (1997) Int. J. Bifurcation Chaos , vol.7 , pp. 2755-2771
    • di Bernardo, M.1    Fossas, E.2    Olivar, G.3    Vasca, F.4
  • 77
    • 0037126508 scopus 로고    scopus 로고
    • Bifurcations in piecewise-smooth feedback systems
    • di Bernardo, M., Garofalo, F., Iannelli, L. and Vasca, F. (2002a). Bifurcations in piecewise-smooth feedback systems, Internat. J. Control 75, 16-17, pp. 1243-1259.
    • (2002) Internat. J. Control , vol.75 , Issue.16-17 , pp. 1243-1259
    • di Bernardo, M.1    Garofalo, F.2    Iannelli, L.3    Vasca, F.4
  • 78
    • 0035297802 scopus 로고    scopus 로고
    • Self-oscillations and sliding in relay feedback systems: Symmetry and bifurcations
    • di Bernardo, M., Johansson, K. and Vasca, F. (2001c). Self-oscillations and sliding in relay feedback systems: Symmetry and bifurcations. Int J. Bifurcation Chaos 11, 4, pp. 1121-1140.
    • (2001) Int J. Bifurcation Chaos , vol.11 , Issue.4 , pp. 1121-1140
    • di Bernardo, M.1    Johansson, K.2    Vasca, F.3
  • 79
    • 0037105976 scopus 로고    scopus 로고
    • Bifurcations of dynamical systems with sliding: Derivation of normal-form mappings
    • di Bernardo, M., Kowalczyk, P. and Nordmark, A. (2002b). Bifurcations of dynamical systems with sliding: Derivation of normal-form mappings. Phys. D 170, pp. 175-205.
    • (2002) Phys. D , vol.170 , pp. 175-205
    • di Bernardo, M.1    Kowalczyk, P.2    Nordmark, A.3
  • 80
    • 0346910377 scopus 로고    scopus 로고
    • Sliding bifurcations: A novel mechanism for the sudden onset of chaos in dry friction oscillators
    • di Bernardo, M., Kowalczyk, P. and Nordmark, A. (2003). Sliding bifurcations: A novel mechanism for the sudden onset of chaos in dry friction oscillators. Int. J. Bifurcation Chaos 13, 10, pp. 2935-2948.
    • (2003) Int. J. Bifurcation Chaos , vol.13 , Issue.10 , pp. 2935-2948
    • di Bernardo, M.1    Kowalczyk, P.2    Nordmark, A.3
  • 81
    • 37149040240 scopus 로고    scopus 로고
    • Discontinuity-induced bifurcations of equilibria in piecewise-smooth and impacting dynamical systems
    • di Bernardo, M., Nordmark, A. and Olivar, G. (2008b). Discontinuity-induced bifurcations of equilibria in piecewise-smooth and impacting dynamical systems. Phys. D 237, pp. 119-136.
    • (2008) Phys. D , vol.237 , pp. 119-136
    • di Bernardo, M.1    Nordmark, A.2    Olivar, G.3
  • 82
    • 33749559250 scopus 로고    scopus 로고
    • A mechanism for dangerous border collision bifurcations
    • Do, Y. (2007). A mechanism for dangerous border collision bifurcations. Chaos Solitons Fractals 32, pp. 352-362.
    • (2007) Chaos Solitons Fractals , vol.32 , pp. 352-362
    • Do, Y.1
  • 83
    • 33749411065 scopus 로고    scopus 로고
    • Dangerous border-collision bifurcations of a piecewise-smooth map
    • Do, Y. and Baek, H. (2006). Dangerous border-collision bifurcations of a piecewise-smooth map. Comm. Pure Appl. Anal. 5, 3, pp. 493-503.
    • (2006) Comm. Pure Appl. Anal. , vol.5 , Issue.3 , pp. 493-503
    • Do, Y.1    Baek, H.2
  • 84
    • 42949104983 scopus 로고    scopus 로고
    • Stability of fixed points placed on the border in the piecewise linear systems
    • Do, Y., Kim, S. and Kim, P. (2008). Stability of fixed points placed on the border in the piecewise linear systems. Chaos Solitons Fractals 38, 2, pp. 391-399.
    • (2008) Chaos Solitons Fractals , vol.38 , Issue.2 , pp. 391-399
    • Do, Y.1    Kim, S.2    Kim, P.3
  • 87
    • 0034300282 scopus 로고    scopus 로고
    • Self-rotation number using the turning angle
    • Dullin, H., Sterling, D. and Meiss, J. (2000). Self-rotation number using the turning angle. Phys. D 145, pp. 25-46.
    • (2000) Phys. D , vol.145 , pp. 25-46
    • Dullin, H.1    Sterling, D.2    Meiss, J.3
  • 89
    • 0038351322 scopus 로고    scopus 로고
    • Multiple attractor bifurcations: A source of unpredictability in piecewise smooth systems
    • Dutta, M., Nusse, H., Ott, E., Yorke, J. and Yuan, G. (1999). Multiple attractor bifurcations: A source of unpredictability in piecewise smooth systems. Phys. Rev. Lett. 83, 21, pp. 4281-4284.
    • (1999) Phys. Rev. Lett. , vol.83 , Issue.21 , pp. 4281-4284
    • Dutta, M.1    Nusse, H.2    Ott, E.3    Yorke, J.4    Yuan, G.5
  • 90
    • 49049119916 scopus 로고    scopus 로고
    • On the existence of low-period orbits in n-dimensional piecewise linear discontinuous maps
    • Dutta, P., Routroy, B., Banerjee, S. and Alam, S. (2008). On the existence of low-period orbits in n-dimensional piecewise linear discontinuous maps. Nonlinear Dynamics 53, pp. 369-380.
    • (2008) Nonlinear Dynamics , vol.53 , pp. 369-380
    • Dutta, P.1    Routroy, B.2    Banerjee, S.3    Alam, S.4
  • 91
    • 1842616169 scopus 로고    scopus 로고
    • Numerical approximation of rough invariant curves of planar maps
    • Edoh, K. and Lorenz, J. (2003). Numerical approximation of rough invariant curves of planar maps, SIAM J. Sci. Comput. 25, 1, pp. 213-223.
    • (2003) SIAM J. Sci. Comput. , vol.25 , Issue.1 , pp. 213-223
    • Edoh, K.1    Lorenz, J.2
  • 92
    • 0034315476 scopus 로고    scopus 로고
    • Analysis of continuous-time switching networks
    • Edwards, R. (2000). Analysis of continuous-time switching networks. Phys. D 146, pp. 165-199.
    • (2000) Phys. D , vol.146 , pp. 165-199
    • Edwards, R.1
  • 93
    • 0035427446 scopus 로고    scopus 로고
    • Homoclinical chaos and the period-adding route to complex non-chaotic attractors in fluidized bed catalytic reactors
    • Elnashaie, S., Harraz, H. and Abashar, M. (2001). Homoclinical chaos and the period-adding route to complex non-chaotic attractors in fluidized bed catalytic reactors. Chaos Solitons Fractals 12, pp. 1761-1792.
    • (2001) Chaos Solitons Fractals , vol.12 , pp. 1761-1792
    • Elnashaie, S.1    Harraz, H.2    Abashar, M.3
  • 96
    • 49849107837 scopus 로고
    • Doubling of the oscillation period with C-bifurcations in piecewise continuous systems
    • Feigin, M. (1970). Doubling of the oscillation period with C-bifurcations in piecewise continuous systems. J. Appl. Math. Mech. 34, 5, pp. 822-830.
    • (1970) J. Appl. Math. Mech. , vol.34 , Issue.5 , pp. 822-830
    • Feigin, M.1
  • 97
    • 49549155020 scopus 로고
    • On the generation of sets of subharmonic modes in a piecewise continuous system
    • Feigin, M. (1974). On the generation of sets of subharmonic modes in a piecewise continuous system. J. Appl. Math. Mech. 38, 5, pp. 759-767.
    • (1974) J. Appl. Math. Mech. , vol.38 , Issue.5 , pp. 759-767
    • Feigin, M.1
  • 98
    • 0018210582 scopus 로고
    • On the structure of C-bifurcation boundaries of piecewise-continuous systems
    • Feigin, M. (1978). On the structure of C-bifurcation boundaries of piecewise-continuous systems. J. Appl. Math. Mech. 42, 5, pp. 885-895.
    • (1978) J. Appl. Math. Mech. , vol.42 , Issue.5 , pp. 885-895
    • Feigin, M.1
  • 99
    • 21344472534 scopus 로고
    • The increasingly complex structure of the bifurcation tree of a piecewise-smooth system
    • Feigin, M. (1995). The increasingly complex structure of the bifurcation tree of a piecewise-smooth system. J. Appl. Math. Mech. 59, 6, pp. 853-863.
    • (1995) J. Appl. Math. Mech. , vol.59 , Issue.6 , pp. 853-863
    • Feigin, M.1
  • 100
    • 0001356311 scopus 로고
    • Persistence and smoothness of invariant manifolds for flows
    • Fenichel, N. (1971). Persistence and smoothness of invariant manifolds for flows. Indiana Univ. Math. J. 21, 3.
    • (1971) Indiana Univ. Math. J , vol.21 , pp. 3
    • Fenichel, N.1
  • 101
    • 0345258030 scopus 로고    scopus 로고
    • Lagrange stability and performance analysis of discrete-time piecewise affine systems with logic states
    • Ferrari-Trecate, G., Cuzzola, F. and Morari, M. (2003). Lagrange stability and performance analysis of discrete-time piecewise affine systems with logic states. Int. J. Control 76, 16, pp. 1585-1598.
    • (2003) Int. J. Control , vol.76 , Issue.16 , pp. 1585-1598
    • Ferrari-Trecate, G.1    Cuzzola, F.2    Morari, M.3
  • 102
    • 84931237371 scopus 로고
    • Regulatory properties of growing cell populations of Saccharomyces cerevisiae in a continuous culture system
    • in A. Kocková-Kratochri-lová (ed.), 16-21 July 1966. (Slovenskej Akadémie Vied, Bratislava)
    • Fiechter, H., A. von Meyenburg (1968). Regulatory properties of growing cell populations of Saccharomyces cerevisiae in a continuous culture system. in A. Kocková-Kratochri-lová (ed.), Yeasts. Proceedings of the 2nd Symposium on Yeasts held in Bratislava, 16-21 July 1966. (Slovenskej Akadémie Vied, Bratislava), pp. 387-398.
    • (1968) Yeasts. Proceedings of the 2nd Symposium on Yeasts held in Bratislava , pp. 387-398
    • Fiechter, H.1    von Meyenburg, A.2
  • 103
    • 0002299782 scopus 로고
    • Differential equations with discontinuous right-hand side
    • (AMS, Ann Arbor)
    • Filippov, A. (1964). Differential equations with discontinuous right-hand side. in American Mathematical Society Translations., Vol. 42 (AMS, Ann Arbor), pp. 199-231.
    • (1964) American Mathematical Society Translations , vol.42 , pp. 199-231
    • Filippov, A.1
  • 107
    • 51249175593 scopus 로고
    • Periodic points and rotation numbers for area preserving diffeomorphisms of the plane
    • Franks, J. (1990). Periodic points and rotation numbers for area preserving diffeomorphisms of the plane. Inst. Hautes Études Sci. Publ. Math. 71, pp. 105-120.
    • (1990) Inst. Hautes Études Sci. Publ. Math , vol.71 , pp. 105-120
    • Franks, J.1
  • 108
    • 33746715031 scopus 로고    scopus 로고
    • Bifurcations caused by grazing incidence in many degrees of freedom impact oscillators
    • Fredriksson, M. and Nordmark, A. (1997). Bifurcations caused by grazing incidence in many degrees of freedom impact oscillators. Proc. R. Soc. A 453, pp. 1261-1276.
    • (1997) Proc. R. Soc. A , vol.453 , pp. 1261-1276
    • Fredriksson, M.1    Nordmark, A.2
  • 109
    • 0032215728 scopus 로고    scopus 로고
    • Bifurcation sets of continuous piecewise linear systems with two zones
    • Freire, E., Ponce, E., Rodrigo, F. and Torres, F. (1998). Bifurcation sets of continuous piecewise linear systems with two zones. Int. J. Bifurcation Chaos 8, 11, pp. 2073-2097.
    • (1998) Int. J. Bifurcation Chaos , vol.8 , Issue.11 , pp. 2073-2097
    • Freire, E.1    Ponce, E.2    Rodrigo, F.3    Torres, F.4
  • 110
    • 17044412070 scopus 로고    scopus 로고
    • A piecewise linear electronic circuit with a multiplicity of bifurcations
    • Freire, E., Ponce, E., Rodrigo, F. and Torres, F. (2004). A piecewise linear electronic circuit with a multiplicity of bifurcations. Int. J. Bifurcation Chaos 14, 11, pp. 3871-3881.
    • (2004) Int. J. Bifurcation Chaos , vol.14 , Issue.11 , pp. 3871-3881
    • Freire, E.1    Ponce, E.2    Rodrigo, F.3    Torres, F.4
  • 111
    • 34248515417 scopus 로고    scopus 로고
    • A biparametric bifurcation in 3D continuous piecewise linear systems with two zones
    • Freire, E., Ponce, E. and Ros, J. (2007). A biparametric bifurcation in 3D continuous piecewise linear systems with two zones. Application to Chua's circuit. Int. J. Bifurcation Chaos. 17, 2, pp. 445-457.
    • (2007) Application to Chua's circuit. Int. J. Bifurcation Chaos. , vol.17 , Issue.2 , pp. 445-457
    • Freire, E.1    Ponce, E.2    Ros, J.3
  • 112
    • 0001116081 scopus 로고    scopus 로고
    • Hopf-like bifurcations in planar piecewise linear systems
    • Freire, E., Ponce, E. and Torres, F. (1997). Hopf-like bifurcations in planar piecewise linear systems, Publicacions Matemátiques 41, pp. 131-148.
    • (1997) Publicacions Matemátiques , vol.41 , pp. 131-148
    • Freire, E.1    Ponce, E.2    Torres, F.3
  • 113
    • 0347544226 scopus 로고    scopus 로고
    • Symbolic analysis for some planar piecewise linear maps
    • Fu, X. and Ashwin, P. (2003). Symbolic analysis for some planar piecewise linear maps. Discrete Contin. Dyn. Syst. 9, 6, pp. 1533-1548.
    • (2003) Discrete Contin. Dyn. Syst. , vol.9 , Issue.6 , pp. 1533-1548
    • Fu, X.1    Ashwin, P.2
  • 116
    • 26944458790 scopus 로고    scopus 로고
    • Dangerous bifurcation at border collision: When does it occur? Phys
    • Ganguli, A. and Banerjee, S. (2005). Dangerous bifurcation at border collision: When does it occur? Phys. Rev. E. 71, 5, p. 057202.
    • (2005) Rev. E. , vol.71 , Issue.5 , pp. 057202
    • Ganguli, A.1    Banerjee, S.2
  • 117
    • 0032054337 scopus 로고    scopus 로고
    • The simplest walking model: stability, complexity, and scaling
    • Garcia, M., Chatterjee, A., Ruina, A. and Coleman, M. (1998). The simplest walking model: stability, complexity, and scaling. ASME J. Biome-chanical Eng. 120, 2, pp. 281-288.
    • (1998) ASME J. Biome-chanical Eng. , vol.120 , Issue.2 , pp. 281-288
    • Garcia, M.1    Chatterjee, A.2    Ruina, A.3    Coleman, M.4
  • 118
    • 85122375695 scopus 로고    scopus 로고
    • private communication
    • Gardini, L. (2008). private communication.
    • (2008)
    • Gardini, L.1
  • 121
    • 0021384431 scopus 로고
    • Solving ordinary differential equations with discontinuities
    • Gear, C. and âsterby, O. (1984). Solving ordinary differential equations with discontinuities. ACM. Trans. Math. Soft. 10, 1, pp. 23-44.
    • (1984) ACM. Trans. Math. Soft. , vol.10 , Issue.1 , pp. 23-44
    • Gear, C.1    âsterby, O.2
  • 122
    • 0035511560 scopus 로고    scopus 로고
    • Planar systems of piecewise linear differential equations with a line of discontinuity
    • Giannakopoulos, F. and Pliete, K. (2001). Planar systems of piecewise linear differential equations with a line of discontinuity. Nonlinearity 14, pp. 1611-1632.
    • (2001) Nonlinearity , vol.14 , pp. 1611-1632
    • Giannakopoulos, F.1    Pliete, K.2
  • 124
    • 28644448264 scopus 로고    scopus 로고
    • Regions of stability for limit cycle oscillations in piecewise linear systems
    • Gonçalves, J. (2005). Regions of stability for limit cycle oscillations in piecewise linear systems. IEEE Trans. Automat. Contr. 50, 11, pp. 1877-1882.
    • (2005) IEEE Trans. Automat. Contr. , vol.50 , Issue.11 , pp. 1877-1882
    • Gonçalves, J.1
  • 125
    • 9144246964 scopus 로고    scopus 로고
    • Global analysis of piecewise linear systems using impact maps and surface Lyapunov functions
    • Gonçalves, J., Megretski, A. and Dahleh, M. (2003). Global analysis of piecewise linear systems using impact maps and surface Lyapunov functions. IEEE Trans. Automat. Contr. 48, 12, pp. 2089-2106.
    • (2003) IEEE Trans. Automat. Contr. , vol.48 , Issue.12 , pp. 2089-2106
    • Gonçalves, J.1    Megretski, A.2    Dahleh, M.3
  • 126
    • 0036938728 scopus 로고    scopus 로고
    • A class of piecewise linear differential equations arising in biological models
    • Gouzé, J. and Sari, T. (2002). A class of piecewise linear differential equations arising in biological models. Dyn. Syst. 17, 4, pp. 299-316.
    • (2002) Dyn. Syst. , vol.17 , Issue.4 , pp. 299-316
    • Gouzé, J.1    Sari, T.2
  • 127
    • 0012349493 scopus 로고
    • Crises, sudden changes in chaotic attractors, and transient chaos
    • Grebogi, C., Ott, E. and Yorke, J. (1983). Crises, sudden changes in chaotic attractors, and transient chaos. Phys. D 7, pp. 181-200.
    • (1983) Phys. D , vol.7 , pp. 181-200
    • Grebogi, C.1    Ott, E.2    Yorke, J.3
  • 128
    • 4243343119 scopus 로고
    • Effective potentials: A new approach and new results for one-dimensional systems with competing length scales
    • Griffiths, R. and Chou, W. (1986). Effective potentials: A new approach and new results for one-dimensional systems with competing length scales. Phys. Rev. Lett. 56, 18, pp. 1929-1931.
    • (1986) Phys. Rev. Lett. , vol.56 , Issue.18 , pp. 1929-1931
    • Griffiths, R.1    Chou, W.2
  • 130
    • 38249014637 scopus 로고
    • Periodic solutions of homogeneous equations
    • Hadeler, K. (1992). Periodic solutions of homogeneous equations. J. Diff. Eq. 95, 1, pp. 183-202.
    • (1992) J. Diff. Eq. , vol.95 , Issue.1 , pp. 183-202
    • Hadeler, K.1
  • 131
    • 0037562825 scopus 로고    scopus 로고
    • C-bifurcations and period-adding in one-dimensional piecewise-smooth maps
    • Halse, C., Homer, M. and di Bernardo, M. (2003). C-bifurcations and period-adding in one-dimensional piecewise-smooth maps. Chaos Solitons Fractals 18, pp. 953-976.
    • (2003) Chaos Solitons Fractals , vol.18 , pp. 953-976
    • Halse, C.1    Homer, M.2    di Bernardo, M.3
  • 132
    • 34447559509 scopus 로고    scopus 로고
    • Coexisting solutions and bifurcations in mechanical oscillations with backlash
    • Halse, C., Wilson, R., di Bernardo, M. and Homer, M. (2007). Coexisting solutions and bifurcations in mechanical oscillations with backlash. J. Sound. Vib. 305, pp. 854-885.
    • (2007) J. Sound. Vib , vol.305 , pp. 854-885
    • Halse, C.1    Wilson, R.2    di Bernardo, M.3    Homer, M.4
  • 136
    • 1642601666 scopus 로고    scopus 로고
    • Robust dangerous border-collision bifurcations in piecewise smooth systems, Phys
    • Hassouneh, M., Abed, E. and Nusse, H. (2004). Robust dangerous border-collision bifurcations in piecewise smooth systems, Phys. Rev. Lett. 92, p. 070201.
    • (2004) Rev. Lett. , vol.92 , pp. 070201
    • Hassouneh, M.1    Abed, E.2    Nusse, H.3
  • 137
    • 3843105974 scopus 로고    scopus 로고
    • The complementarity class of hybrid dynamical systems
    • Heemels, W. and Brogliato, B. (2003). The complementarity class of hybrid dynamical systems. Euro. J. Control 9, pp. 322-360.
    • (2003) Euro. J. Control , vol.9 , pp. 322-360
    • Heemels, W.1    Brogliato, B.2
  • 139
    • 0041304646 scopus 로고    scopus 로고
    • Dynamic modeling and control of yeast cell populations in continuous biochemical reactors
    • Henson, M. (2003). Dynamic modeling and control of yeast cell populations in continuous biochemical reactors. Comput. Chem. Eng. 27, pp. 1185-1199.
    • (2003) Comput. Chem. Eng , vol.27 , pp. 1185-1199
    • Henson, M.1
  • 141
    • 0028257207 scopus 로고
    • Slender rigid block motion
    • Hogan, S. (1994). Slender rigid block motion. J. Eng. Mech. 120, 1, pp. 11-24.
    • (1994) J. Eng. Mech. , vol.120 , Issue.1 , pp. 11-24
    • Hogan, S.1
  • 142
    • 34547372156 scopus 로고    scopus 로고
    • Dynamics of a piecewise linear map with a gap
    • Hogan, S., Higham, L. and Griffin, T. (2007). Dynamics of a piecewise linear map with a gap. Proc. R. Soc. A 463, pp. 49-65.
    • (2007) Proc. R. Soc. A , vol.463 , pp. 49-65
    • Hogan, S.1    Higham, L.2    Griffin, T.3
  • 143
    • 0000732703 scopus 로고
    • From simple to complex oscillatory behaviour via intermittent chaos in the Rose-Hindmarsh model for neuronal activity
    • Holden, A. and Fan, Y. (1992). From simple to complex oscillatory behaviour via intermittent chaos in the Rose-Hindmarsh model for neuronal activity. Chaos Solitons Fractals 2, 4, pp. 349-369.
    • (1992) Chaos Solitons Fractals , vol.2 , Issue.4 , pp. 349-369
    • Holden, A.1    Fan, Y.2
  • 144
    • 0007382289 scopus 로고
    • \Period three to period two" bifurcation for piecewise linear models
    • Hommes, C. and Nusse, H. (1991). \Period three to period two" bifurcation for piecewise linear models. J. Economics 54, 2, pp. 157-169.
    • (1991) J. Economics , vol.54 , Issue.2 , pp. 157-169
    • Hommes, C.1    Nusse, H.2
  • 146
    • 0008272025 scopus 로고    scopus 로고
    • Stability of periodic motions with impacts
    • in B. Brogliato (ed.), Springer-Verlag, New York
    • Ivanov, A. (2000). Stability of periodic motions with impacts. in B. Brogliato (ed.), Impacts in Mechanical Systems: Analysis and Modelling. (Springer-Verlag, New York).
    • (2000) Impacts in Mechanical Systems: Analysis and Modelling
    • Ivanov, A.1
  • 147
    • 33747754136 scopus 로고    scopus 로고
    • Stability tests and stabilization for piece-wise linear systems based on poles and zeros of subsystems
    • Iwatani, Y. and Shinji, H. (2006). Stability tests and stabilization for piece-wise linear systems based on poles and zeros of subsystems. Automatica 42, pp. 1685-1695.
    • (2006) Automatica , vol.42 , pp. 1685-1695
    • Iwatani, Y.1    Shinji, H.2
  • 148
    • 1442335935 scopus 로고    scopus 로고
    • Border-collision bifurcations in one-dimensional discontinuous maps
    • Jain, P. and Banerjee, S. (2003). Border-collision bifurcations in one-dimensional discontinuous maps. Int. J. Bifurcation Chaos 13, 11, pp. 3341-3351.
    • (2003) Int. J. Bifurcation Chaos , vol.13 , Issue.11 , pp. 3341-3351
    • Jain, P.1    Banerjee, S.2
  • 151
    • 0032875981 scopus 로고    scopus 로고
    • Cybernetic model of the growth dynamics of Saccharomyces cerevisiae in batch and continuous cultures
    • Jones, K. and Kompala, D. (1999). Cybernetic model of the growth dynamics of Saccharomyces cerevisiae in batch and continuous cultures, J. Biotech. 71, pp. 105-131.
    • (1999) J. Biotech , vol.71 , pp. 105-131
    • Jones, K.1    Kompala, D.2
  • 152
    • 0033279399 scopus 로고    scopus 로고
    • High-level canonical piecewise linear representation using a simplicial partition
    • Julián, P., Desages, A. and Agamennoni, O. (1999). High-level canonical piecewise linear representation using a simplicial partition. IEEE Trans. Circuits Systems I Fund. Theory Appl. 46, 4, pp. 463-480.
    • (1999) IEEE Trans. Circuits Systems I Fund. Theory Appl , vol.46 , Issue.4 , pp. 463-480
    • Julián, P.1    Desages, A.2    Agamennoni, O.3
  • 153
    • 0018035219 scopus 로고
    • A global representation of multidimensional piecewise-linear functions with linear partitions
    • Kang, S. and Chua, L. (1978). A global representation of multidimensional piecewise-linear functions with linear partitions. IEEE Trans. Circuits Systems CAS-25, 11, pp. 938-940.
    • (1978) IEEE Trans. Circuits Systems CAS-25 , vol.11 , pp. 938-940
    • Kang, S.1    Chua, L.2
  • 154
    • 11744278171 scopus 로고    scopus 로고
    • Multiple choice bifurcations as a source of unpredictability in dynamical systems
    • Kapitaniak, T. and Maistrenko, Y. (1998). Multiple choice bifurcations as a source of unpredictability in dynamical systems. Phys. Rev. E 58, 4, pp. 5161-5163.
    • (1998) Phys. Rev. E , vol.58 , Issue.4 , pp. 5161-5163
    • Kapitaniak, T.1    Maistrenko, Y.2
  • 155
    • 0040625923 scopus 로고    scopus 로고
    • Riddling bifurcations in coupled piecewise linear maps
    • Kapitaniak, T. and Maistrenko, Y. (1999). Riddling bifurcations in coupled piecewise linear maps. Phys. D 126, pp. 18-26.
    • (1999) Phys. D , vol.126 , pp. 18-26
    • Kapitaniak, T.1    Maistrenko, Y.2
  • 156
    • 0242682618 scopus 로고    scopus 로고
    • Period adding and broken Farey tree sequence of bifurcations for mixed-mode oscillations and chaos in the simplest three-variable nonlinear system
    • Kawczyński, A. and Strizhak, P. (2000). Period adding and broken Farey tree sequence of bifurcations for mixed-mode oscillations and chaos in the simplest three-variable nonlinear system. J. Chem. Phys. 112, 14, pp. 6122-6130.
    • (2000) J. Chem. Phys. , vol.112 , Issue.14 , pp. 6122-6130
    • Kawczyński, A.1    Strizhak, P.2
  • 158
    • 18644382642 scopus 로고    scopus 로고
    • Bifurcations in glass networks
    • Killough, D. and Edwards, R. (2005). Bifurcations in glass networks. Int. J. Bifurcation Chaos 15, 2, pp. 395-423.
    • (2005) Int. J. Bifurcation Chaos , vol.15 , Issue.2 , pp. 395-423
    • Killough, D.1    Edwards, R.2
  • 159
  • 160
    • 0022755363 scopus 로고
    • Investigation of bacterial growth on mixed substrates: Experimental evaluation of cybernetic models
    • Kompala, D., Ramkrishna, D., Jansen, N. and Tsao, G. (1986). Investigation of bacterial growth on mixed substrates: Experimental evaluation of cybernetic models. Biotech. Bioeng. 28, pp. 1044-1055.
    • (1986) Biotech. Bioeng , vol.28 , pp. 1044-1055
    • Kompala, D.1    Ramkrishna, D.2    Jansen, N.3    Tsao, G.4
  • 161
    • 0021531929 scopus 로고
    • Cybernetic modelling of microbial growth on multiple substrates
    • Kompala, D., Ramkrishna, D. and Tsao, G. (1984). Cybernetic modelling of microbial growth on multiple substrates. Biotech. Bioeng. 26, pp. 1272-1281.
    • (1984) Biotech. Bioeng , vol.26 , pp. 1272-1281
    • Kompala, D.1    Ramkrishna, D.2    Tsao, G.3
  • 162
    • 14844336939 scopus 로고    scopus 로고
    • Robust chaos and border-collision bifurcations in non-invertible piecewise-linear maps
    • Kowalczyk, P. (2005). Robust chaos and border-collision bifurcations in non-invertible piecewise-linear maps. Nonlinearity 18, pp. 485-504.
    • (2005) Nonlinearity , vol.18 , pp. 485-504
    • Kowalczyk, P.1
  • 163
    • 19744377598 scopus 로고    scopus 로고
    • Two-parameter degenerate sliding bifurcations in Filippov systems
    • Kowalczyk, P. and di Bernardo, M. (2005). Two-parameter degenerate sliding bifurcations in Filippov systems. Phys. D 204, pp. 204-229.
    • (2005) Phys. D , vol.204 , pp. 204-229
    • Kowalczyk, P.1    di Bernardo, M.2
  • 165
    • 43049133262 scopus 로고    scopus 로고
    • Two-parameter sliding bifurcations of periodic solutions in a dry-friction oscillator
    • Kowalczyk, P. and Piiroinen, P. (2008). Two-parameter sliding bifurcations of periodic solutions in a dry-friction oscillator. Phys. D 237, pp. 1053-1073.
    • (2008) Phys. D , vol.237 , pp. 1053-1073
    • Kowalczyk, P.1    Piiroinen, P.2
  • 166
    • 0035839416 scopus 로고    scopus 로고
    • Relaxation oscillation and canard explosion
    • Krupa, M. and Szmolyan, P. (2001). Relaxation oscillation and canard explosion. J. Diff. Eq. 174, pp. 312-368.
    • (2001) J. Diff. Eq , vol.174 , pp. 312-368
    • Krupa, M.1    Szmolyan, P.2
  • 167
    • 55949108104 scopus 로고    scopus 로고
    • Nonlinear analysis of the effect of maintenance in continuous cell cultures
    • Kumar, M., Kienle, A., Zeyer, K. and Pushpavanam, S. (2008). Nonlinear analysis of the effect of maintenance in continuous cell cultures. Math. Comput. Simulation 79, 3, pp. 728-748.
    • (2008) Math. Comput. Simulation , vol.79 , Issue.3 , pp. 728-748
    • Kumar, M.1    Kienle, A.2    Zeyer, K.3    Pushpavanam, S.4
  • 168
    • 56949100992 scopus 로고    scopus 로고
    • Invariant cones for non-smooth dynamical systems
    • Käupper, T. (2008). Invariant cones for non-smooth dynamical systems. Math. Comput. Simulation 79, 4, pp. 1396-1408.
    • (2008) Math. Comput. Simulation , vol.79 , Issue.4 , pp. 1396-1408
    • Käupper, T.1
  • 169
    • 57249084558 scopus 로고    scopus 로고
    • Generalized Hopf bifurcation for non-smooth planar systems
    • Käupper, T. and Moritz, S. (2001). Generalized Hopf bifurcation for non-smooth planar systems. Phil. Trans. R. Soc. Lond. A 359, pp. 2483-2496.
    • (2001) Phil. Trans. R. Soc. Lond. A , vol.359 , pp. 2483-2496
    • Käupper, T.1    Moritz, S.2
  • 171
    • 0242414775 scopus 로고    scopus 로고
    • One-parameter bifurcations in planar Filippov systems
    • Kuznetsov, Y., Rinaldi, S. and Gragnani, A. (2003). One-parameter bifurcations in planar Filippov systems. Int. J. Bifurcation Chaos 13, 8, pp. 2157-2188.
    • (2003) Int. J. Bifurcation Chaos , vol.13 , Issue.8 , pp. 2157-2188
    • Kuznetsov, Y.1    Rinaldi, S.2    Gragnani, A.3
  • 172
    • 27744542697 scopus 로고    scopus 로고
    • Dynamics of a family of piecewise-linear area-preserving plane maps
    • Lagarias, J. and Rains, E. (2005a). Dynamics of a family of piecewise-linear area-preserving plane maps. I. rational rotation numbers. J. Difference Eqn. Appl. 11, 12, pp. 1089-1108.
    • (2005) I. rational rotation numbers. J. Difference Eqn. Appl. , vol.11 , Issue.12 , pp. 1089-1108
    • Lagarias, J.1    Rains, E.2
  • 173
    • 32644459743 scopus 로고    scopus 로고
    • Dynamics of a family of piecewise-linear area-preserving plane maps
    • Lagarias, J. and Rains, E. (2005b). Dynamics of a family of piecewise-linear area-preserving plane maps. II. invariant circles. J. Difference Eqn. Appl. 11, 13, pp. 1137-1163.
    • (2005) II. invariant circles. J. Difference Eqn. Appl. , vol.11 , Issue.13 , pp. 1137-1163
    • Lagarias, J.1    Rains, E.2
  • 174
    • 0029301829 scopus 로고
    • A walk along the branches of the extended Farey tree
    • Lagarias, J. and Tresser, C. (1995). A walk along the branches of the extended Farey tree. IBM J. Res. Dev. 39, 3, pp. 283-294.
    • (1995) IBM J. Res. Dev. , vol.39 , Issue.3 , pp. 283-294
    • Lagarias, J.1    Tresser, C.2
  • 175
    • 23044461899 scopus 로고    scopus 로고
    • Border-collision bifurcations in a dynamic management game
    • Laugesen, J. and Mosekilde, E. (2006). Border-collision bifurcations in a dynamic management game. Comput. Oper. Res. 33, pp. 464-478.
    • (2006) Comput. Oper. Res , vol.33 , pp. 464-478
    • Laugesen, J.1    Mosekilde, E.2
  • 177
    • 33646852290 scopus 로고    scopus 로고
    • Rotation numbers in the infinite annulus
    • Le Calvez, P. (2001). Rotation numbers in the infinite annulus. Proc. Amer. Math. Soc. 129, 11, pp. 3221-3230.
    • (2001) Proc. Amer. Math. Soc. , vol.129 , Issue.11 , pp. 3221-3230
    • Le Calvez, P.1
  • 179
    • 0004132025 scopus 로고
    • Prentice Hall, Englewood Cliffs, NJ
    • Lee, J. (1992). Biochemical Engineering. (Prentice Hall, Englewood Cliffs, NJ).
    • (1992) Biochemical Engineering
    • Lee, J.1
  • 180
    • 33750069186 scopus 로고    scopus 로고
    • Bifurcations of equilibria in non-smooth continuous systems
    • Leine, R. (2006). Bifurcations of equilibria in non-smooth continuous systems. Phys. D 223, pp. 121-137.
    • (2006) Phys. D , vol.223 , pp. 121-137
    • Leine, R.1
  • 182
    • 0037119532 scopus 로고    scopus 로고
    • Discontinuous bifurcations of periodic solutions
    • Leine, R. and Van Campen, D. (2002). Discontinuous bifurcations of periodic solutions. Math. Comput. Model. 36, pp. 259-273.
    • (2002) Math. Comput. Model , vol.36 , pp. 259-273
    • Leine, R.1    Van Campen, D.2
  • 183
  • 184
    • 23944439910 scopus 로고    scopus 로고
    • Heteroclinic bifurcations and optimal control in the nonlinear rocking dynamics of generic and slender rigid blocks
    • Lenci, S. and Rega, G. (2005). Heteroclinic bifurcations and optimal control in the nonlinear rocking dynamics of generic and slender rigid blocks. Int. J. Bifurcation Chaos 15, 6, pp. 1901-1918.
    • (2005) Int. J. Bifurcation Chaos , vol.15 , Issue.6 , pp. 1901-1918
    • Lenci, S.1    Rega, G.2
  • 185
    • 0000100336 scopus 로고
    • Period three implies chaos
    • Li, T. and Yorke, J. (1975). Period three implies chaos. Amer. Math. Monthly. 82, 10, pp. 985-992.
    • (1975) Amer. Math. Monthly. , vol.82 , Issue.10 , pp. 985-992
    • Li, T.1    Yorke, J.2
  • 186
    • 84968518885 scopus 로고
    • Ergodic transformations from an interval into itself
    • Li, T. and Yorke, J. (1978). Ergodic transformations from an interval into itself. Trans. Amer. Math. Soc. 235, 1, pp. 183-192.
    • (1978) Trans. Amer. Math. Soc. , vol.235 , Issue.1 , pp. 183-192
    • Li, T.1    Yorke, J.2
  • 187
    • 0035507335 scopus 로고    scopus 로고
    • A canonical representation of high-dimensional continuous piecewise-linear functions
    • Li, X., Wang, S. and Yin, W. (2001). A canonical representation of high-dimensional continuous piecewise-linear functions. IEEE Trans. Circuits Systems I Fund. Theory Appl. 48, 11, pp. 1347-1351.
    • (2001) IEEE Trans. Circuits Systems I Fund. Theory Appl. , vol.48 , Issue.11 , pp. 1347-1351
    • Li, X.1    Wang, S.2    Yin, W.3
  • 188
    • 0027334453 scopus 로고
    • Free rocking of prismatic blocks
    • Lipscombe, P. and Pellegrino, S. (1993). Free rocking of prismatic blocks. J. Eng. Mech. 119, 7, pp. 1387-1410.
    • (1993) J. Eng. Mech. , vol.119 , Issue.7 , pp. 1387-1410
    • Lipscombe, P.1    Pellegrino, S.2
  • 189
    • 34250212162 scopus 로고    scopus 로고
    • Horseshoes near homoclinic orbits for piecewise linear differential systems in R3
    • Llibre, J., Ponce, E. and Teruel, A. (2007). Horseshoes near homoclinic orbits for piecewise linear differential systems in R3. Int. J. Bifurcation Chaos 17, 4, pp. 1171-1184.
    • (2007) Int. J. Bifurcation Chaos , vol.17 , Issue.4 , pp. 1171-1184
    • Llibre, J.1    Ponce, E.2    Teruel, A.3
  • 190
    • 0030296063 scopus 로고    scopus 로고
    • Phase portraits of planar control systems
    • Llibre, J. and Sotomayor, J. (1996). Phase portraits of planar control systems. Nonlin. Anal. TMA 27, 10, pp. 1177-1197.
    • (1996) Nonlin. Anal. TMA , vol.27 , Issue.10 , pp. 1177-1197
    • Llibre, J.1    Sotomayor, J.2
  • 191
    • 4944253830 scopus 로고    scopus 로고
    • Existence of Poincaré maps in piecewise linear differential systems in Rn
    • Llibre, J. and Teruel, A. (2004). Existence of Poincaré maps in piecewise linear differential systems in Rn. Int. J. Bifurcation Chaos 14, 8, pp. 2843-2851.
    • (2004) Int. J. Bifurcation Chaos , vol.14 , Issue.8 , pp. 2843-2851
    • Llibre, J.1    Teruel, A.2
  • 192
    • 22144485576 scopus 로고    scopus 로고
    • A symmetric piecewise-linear chaotic system with a single equilibrium point
    • López, R., Rodri-guez, M., Granero, M., Ojeda, J. and Bruzón, E. (2005). A symmetric piecewise-linear chaotic system with a single equilibrium point. Int. J. Bifurcation Chaos 15, 4, pp. 1411-1415.
    • (2005) Int. J. Bifurcation Chaos , vol.15 , Issue.4 , pp. 1411-1415
    • López, R.1    Rodri-guez, M.2    Granero, M.3    Ojeda, J.4    Bruzón, E.5
  • 194
    • 0026155243 scopus 로고
    • Global properties of continuous piecewise linear vector-fields
    • Lum, R. and Chua, L. (1991). Global properties of continuous piecewise linear vector-fields. 1. Simplest case in R2. Int. J. Circ. Theor. Appl. 19, 3, pp. 251-307.
    • (1991) 1. Simplest case in R2. Int. J. Circ. Theor. Appl. , vol.19 , Issue.3 , pp. 251-307
    • Lum, R.1    Chua, L.2
  • 195
    • 0030150205 scopus 로고    scopus 로고
    • The dynamics of a bouncing ball with a sinu-soidally vibrating table revisited
    • Luo, A. and Han, R. (1996). The dynamics of a bouncing ball with a sinu-soidally vibrating table revisited. Nonlinear Dynamics 10, 1, pp. 1-18.
    • (1996) Nonlinear Dynamics , vol.10 , Issue.1 , pp. 1-18
    • Luo, A.1    Han, R.2
  • 196
    • 33646344688 scopus 로고    scopus 로고
    • Border collision bifurcations in a soft impact system
    • Ma, Y., Agarwal, M. and Banerjee, S. (2006). Border collision bifurcations in a soft impact system. Phys. Lett. A 354, pp. 281-287.
    • (2006) Phys. Lett. A , vol.354 , pp. 281-287
    • Ma, Y.1    Agarwal, M.2    Banerjee, S.3
  • 199
    • 21844516243 scopus 로고
    • Bifurcations of attracting cycles from time-delayed Chua's circiut
    • Maistrenko, Y., Maistrenko, V., Vikul, S. and Chua, L. (1995). Bifurcations of attracting cycles from time-delayed Chua's circiut. Int. J. Bifurcation Chaos. 5, 3, pp. 653-671.
    • (1995) Int. J. Bifurcation Chaos. , vol.5 , Issue.3 , pp. 653-671
    • Maistrenko, Y.1    Maistrenko, V.2    Vikul, S.3    Chua, L.4
  • 200
    • 0032131474 scopus 로고    scopus 로고
    • About two mechanisms of reunion of chaotic attractors
    • Maistrenko, Y., Sushko, I. and Gardini, L. (1998). About two mechanisms of reunion of chaotic attractors. Chaos Solitons Fractals 9, 8, pp. 1373-1390.
    • (1998) Chaos Solitons Fractals , vol.9 , Issue.8 , pp. 1373-1390
    • Maistrenko, Y.1    Sushko, I.2    Gardini, L.3
  • 202
    • 0015858113 scopus 로고
    • On finite limit sets for transformations on the unit interval
    • Metropolis, N., Stein, M. and Stein, P. (1973). On finite limit sets for transformations on the unit interval. J. Comb. Theor. A15, p. 25.
    • (1973) J. Comb. Theor. A15 , pp. 25
    • Metropolis, N.1    Stein, M.2    Stein, P.3
  • 203
    • 0000848698 scopus 로고
    • On iterated maps of the interval
    • in A. Dold and B. Eckmann (eds.), (Springer-Verlag, New York)
    • Milnor, J. and Thurston, W. (1988). On iterated maps of the interval. in A. Dold and B. Eckmann (eds.), Lect. Notes. in Math., Vol. 1342 (Springer-Verlag, New York), pp. 465-563.
    • (1988) Lect. Notes. in Math , vol.1342 , pp. 465-563
    • Milnor, J.1    Thurston, W.2
  • 206
    • 36349037270 scopus 로고    scopus 로고
    • Nonlinear dynamic phenomena in the beer model
    • Mosekilde, E. and Laugesen, J. (2007). Nonlinear dynamic phenomena in the beer model. Syst. Dyn. Rev. 23, pp. 229-252.
    • (2007) Syst. Dyn. Rev , vol.23 , pp. 229-252
    • Mosekilde, E.1    Laugesen, J.2
  • 208
    • 0035828739 scopus 로고    scopus 로고
    • Multiplicity and stability of steady states in continuous bioreactors: Dissection of cybernetic models
    • Namjoshi, A. and Ramkrishna, D. (2001). Multiplicity and stability of steady states in continuous bioreactors: Dissection of cybernetic models. Chem. Eng. Sci. 56, 19, pp. 5593-5607.
    • (2001) Chem. Eng. Sci. , vol.56 , Issue.19 , pp. 5593-5607
    • Namjoshi, A.1    Ramkrishna, D.2
  • 210
    • 4244118801 scopus 로고    scopus 로고
    • Universal limit mapping in grazing bifurcations
    • Nordmark, A. (1997). Universal limit mapping in grazing bifurcations. Phys. Rev. E 55, 1, pp. 266-270.
    • (1997) Phys. Rev. E , vol.55 , Issue.1 , pp. 266-270
    • Nordmark, A.1
  • 211
    • 0035511360 scopus 로고    scopus 로고
    • Existence of periodic orbits in grazing bifurcations of impacting mechanical oscillators
    • Nordmark, A. (2001). Existence of periodic orbits in grazing bifurcations of impacting mechanical oscillators. Nonlinearity 14, pp. 1517-1542.
    • (2001) Nonlinearity , vol.14 , pp. 1517-1542
    • Nordmark, A.1
  • 212
    • 29144489480 scopus 로고    scopus 로고
    • A codimension-two scenario of sliding solution in grazing-sliding bifurcations
    • Nordmark, A. and Kowalczyk, P. (2006). A codimension-two scenario of sliding solution in grazing-sliding bifurcations. Nonlinearity 19, 1, pp. 1-26.
    • (2006) Nonlinearity , vol.19 , Issue.1 , pp. 1-26
    • Nordmark, A.1    Kowalczyk, P.2
  • 213
    • 0001050846 scopus 로고
    • Border-collision bifurcations: An explanation for observed bifurcation phenomena
    • Nusse, H., Ott, E. and Yorke, J. (1994). Border-collision bifurcations: An explanation for observed bifurcation phenomena. Phys. Rev. E 49, 2, pp. 1073-1076.
    • (1994) Phys. Rev. E , vol.49 , Issue.2 , pp. 1073-1076
    • Nusse, H.1    Ott, E.2    Yorke, J.3
  • 214
    • 44049121950 scopus 로고
    • Border-collision bifurcations including\period two to period three" for piecewise smooth systems
    • Nusse, H. and Yorke, J. (1992). Border-collision bifurcations including\period two to period three" for piecewise smooth systems. Phys. D 57, pp. 39-57.
    • (1992) Phys. D , vol.57 , pp. 39-57
    • Nusse, H.1    Yorke, J.2
  • 215
    • 4344639901 scopus 로고
    • Border-collision bifurcations for piecewise-smooth one-dimensional maps
    • Nusse, H. and Yorke, J. (1995). Border-collision bifurcations for piecewise-smooth one-dimensional maps. Int. J. Bifurcation Chaos. 5, 1, pp. 189-207.
    • (1995) Int. J. Bifurcation Chaos. , vol.5 , Issue.1 , pp. 189-207
    • Nusse, H.1    Yorke, J.2
  • 216
    • 57249110724 scopus 로고    scopus 로고
    • Corner-impact bifurcations: A novel class of discontinuity-induced bifurcations in cam-follower systems
    • Osorio, G., di Bernardo, M. and Santini, S. (2008). Corner-impact bifurcations: A novel class of discontinuity-induced bifurcations in cam-follower systems. SIAM J. Appl. Dyn. Sys. 7, 1, pp. 18-38.
    • (2008) SIAM J. Appl. Dyn. Sys. , vol.7 , Issue.1 , pp. 18-38
    • Osorio, G.1    di Bernardo, M.2    Santini, S.3
  • 217
    • 0003582543 scopus 로고
    • Cambridge University Press, New York
    • Ott, E. (1993). Chaos in Dynamical Systems. (Cambridge University Press, New York).
    • (1993) Chaos in Dynamical Systems
    • Ott, E.1
  • 218
    • 0000685159 scopus 로고
    • The necessity of the Hopf bifurcation for periodically forced oscillators
    • Peckham, B. (1990). The necessity of the Hopf bifurcation for periodically forced oscillators. Nonlinearity 3, 2, pp. 261-280.
    • (1990) Nonlinearity , vol.3 , Issue.2 , pp. 261-280
    • Peckham, B.1
  • 220
    • 0027114979 scopus 로고
    • Transition to chaotic motion in mechanical systems with impacts
    • Peterka, F. and Vacik, J. (1992). Transition to chaotic motion in mechanical systems with impacts. J. Sound Vib. 154, 1, pp. 95-115.
    • (1992) J. Sound Vib. , vol.154 , Issue.1 , pp. 95-115
    • Peterka, F.1    Vacik, J.2
  • 221
    • 3042587897 scopus 로고    scopus 로고
    • Period-adding bifurcations and chaos in a bubble column
    • Piassi, V., Tufaile, A. and Sartorelli, J. (2004). Period-adding bifurcations and chaos in a bubble column. Chaos 14, 2, pp. 477-486.
    • (2004) Chaos , vol.14 , Issue.2 , pp. 477-486
    • Piassi, V.1    Tufaile, A.2    Sartorelli, J.3
  • 222
    • 84867939245 scopus 로고    scopus 로고
    • Chaos and period-adding: Experimental and numerical verification of the grazing bifurcation
    • Piiroinen, P., Virgin, L. and Champneys, A. (2004). Chaos and period-adding: Experimental and numerical verification of the grazing bifurcation. J. Nonlinear Sci. 14, 4, pp. 383-404.
    • (2004) J. Nonlinear Sci. , vol.14 , Issue.4 , pp. 383-404
    • Piiroinen, P.1    Virgin, L.2    Champneys, A.3
  • 223
    • 13244279645 scopus 로고    scopus 로고
    • Analysis and generic properties of gene regulatory networks with graded response functions
    • Plahte, E. and Kjoglum., S. (2005). Analysis and generic properties of gene regulatory networks with graded response functions. Phys. D 201, pp. 150-176.
    • (2005) Phys. D , vol.201 , pp. 150-176
    • Plahte, E.1    Kjoglum, S.2
  • 224
    • 23044528362 scopus 로고    scopus 로고
    • Non-smooth mechanical systems
    • Popp, K. (2000). Non-smooth mechanical systems. J. Appl. Math. Mech. 64, 5, pp. 765-772.
    • (2000) J. Appl. Math. Mech. , vol.64 , Issue.5 , pp. 765-772
    • Popp, K.1
  • 225
    • 0024278876 scopus 로고
    • Oscillations in continuous cultures of budding yeast: A segregated parameter anaylsis
    • Porro, D., Martegani, E., Ranzi, B. and Alberghina, L. (1988). Oscillations in continuous cultures of budding yeast: A segregated parameter anaylsis. Biotech. Bioeng. 32, pp. 411-417.
    • (1988) Biotech. Bioeng , vol.32 , pp. 411-417
    • Porro, D.1    Martegani, E.2    Ranzi, B.3    Alberghina, L.4
  • 226
    • 33644891663 scopus 로고    scopus 로고
    • On the change of periodicities in the Hicksian multiplier-accelerator model with a consumption floor
    • Puu, T., Gardini, L. and Sushko, I. (2006). On the change of periodicities in the Hicksian multiplier-accelerator model with a consumption floor. Chaos Solitons Fractals 29, pp. 681-696.
    • (2006) Chaos Solitons Fractals , vol.29 , pp. 681-696
    • Puu, T.1    Gardini, L.2    Sushko, I.3
  • 229
    • 0023422835 scopus 로고
    • Are microbes optimal strategists? Biotech
    • Ramkrishna, D., Kompala, D. and Tsao, G. (1987). Are microbes optimal strategists? Biotech. Prog. 3, pp. 121-126.
    • (1987) Prog , vol.3 , pp. 121-126
    • Ramkrishna, D.1    Kompala, D.2    Tsao, G.3
  • 230
    • 0141783646 scopus 로고    scopus 로고
    • The rhythm of yeast
    • Richard, P. (2003). The rhythm of yeast. FEMS Microbiol. Rev. 27, p. 547:557.
    • (2003) FEMS Microbiol. Rev. , vol.27 , pp. 547-557
    • Richard, P.1
  • 234
    • 43949104403 scopus 로고    scopus 로고
    • Border collision bifurcations in three-dimensional piecewise smooth systems
    • Roy, I. and Roy, A. (2008). Border collision bifurcations in three-dimensional piecewise smooth systems. Int. J. Bifurcation Chaos 18, 2, pp. 577-586.
    • (2008) Int. J. Bifurcation Chaos , vol.18 , Issue.2 , pp. 577-586
    • Roy, I.1    Roy, A.2
  • 235
    • 0026492327 scopus 로고
    • Oscillatory metabolism of Saccharomyces cerevisiae in continuous culture
    • Satroutdinov, A., Kuriyama, H. and Kobayashi, H. (1992). Oscillatory metabolism of Saccharomyces cerevisiae in continuous culture. FEMS Microbiol. Lett. 98, pp. 261-268.
    • (1992) FEMS Microbiol. Lett , vol.98 , pp. 261-268
    • Satroutdinov, A.1    Kuriyama, H.2    Kobayashi, H.3
  • 236
    • 0000720459 scopus 로고
    • Asymptotic cycles
    • Schwartzman, S. (1957). Asymptotic cycles. Annals of Math. 66, 2, pp. 270-284.
    • (1957) Annals of Math. , vol.66 , Issue.2 , pp. 270-284
    • Schwartzman, S.1
  • 237
    • 27544508068 scopus 로고    scopus 로고
    • Bifurcations and chaos in time delayed piecewise linear dynamical systems
    • Senthilkumar, D. and Lakshmanan, M. (2005). Bifurcations and chaos in time delayed piecewise linear dynamical systems. Int. J. Bifurcation Chaos 15, 9, pp. 2895-2912.
    • (2005) Int. J. Bifurcation Chaos , vol.15 , Issue.9 , pp. 2895-2912
    • Senthilkumar, D.1    Lakshmanan, M.2
  • 239
    • 0038688307 scopus 로고
    • Co-existence of cycles of a continuous map of the line to itself
    • translation of Ukrain. Mat. Z., 16:61-71, 1964
    • Sharkovskii, A. (1995). Co-existence of cycles of a continuous map of the line to itself. Int. J. Bifurcation Chaos 5, 5, pp. 1263-1273, translation of Ukrain. Mat. Z., 16:61-71, 1964.
    • (1995) Int. J. Bifurcation Chaos , vol.5 , Issue.5 , pp. 1263-1273
    • Sharkovskii, A.1
  • 240
    • 33846103882 scopus 로고    scopus 로고
    • Dynamics of delayed relay systems
    • Sieber, J. (2006). Dynamics of delayed relay systems. Nonlinearity 19, 11, pp. 2489-2527.
    • (2006) Nonlinearity , vol.19 , Issue.11 , pp. 2489-2527
    • Sieber, J.1
  • 242
    • 0002224742 scopus 로고
    • A decoding problem in dynamics and in number theory
    • Siegel, R., Tresser, C. and Zettler, G. (1992). A decoding problem in dynamics and in number theory. Chaos 2, 4, pp. 473-493.
    • (1992) Chaos , vol.2 , Issue.4 , pp. 473-493
    • Siegel, R.1    Tresser, C.2    Zettler, G.3
  • 245
    • 60249092217 scopus 로고    scopus 로고
    • Discontinuity induced bifurcations in a model of Saccharomyces cerevisiae
    • Simpson, D., Kompala, D. and Meiss, J. (2009). Discontinuity induced bifurcations in a model of Saccharomyces cerevisiae. Math. Biosci. 218, 1, pp. 40-49.
    • (2009) Math. Biosci. , vol.218 , Issue.1 , pp. 40-49
    • Simpson, D.1    Kompala, D.2    Meiss, J.3
  • 246
    • 35448931206 scopus 로고    scopus 로고
    • Andronov-Hopf bifurcations in planar, piecewise-smooth, continuous flows
    • Simpson, D. and Meiss, J. (2007). Andronov-Hopf bifurcations in planar, piecewise-smooth, continuous flows. Phys. Lett. A 371, 3, pp. 213-220.
    • (2007) Phys. Lett. A , vol.371 , Issue.3 , pp. 213-220
    • Simpson, D.1    Meiss, J.2
  • 247
    • 55849140458 scopus 로고    scopus 로고
    • Neimark-Sacker bifurcations in planar, piecewise-smooth, continuous maps
    • Simpson, D. and Meiss, J. (2008a). Neimark-Sacker bifurcations in planar, piecewise-smooth, continuous maps. SIAM J. Appl. Dyn. Sys. 7, 3, pp. 795-824.
    • (2008) SIAM J. Appl. Dyn. Sys. , vol.7 , Issue.3 , pp. 795-824
    • Simpson, D.1    Meiss, J.2
  • 248
    • 54749100430 scopus 로고    scopus 로고
    • Unfolding a codimension-two discontinuous Andronov-Hopf bifurcation
    • Simpson, D. and Meiss, J. (2008b). Unfolding a codimension-two discontinuous Andronov-Hopf bifurcation. Chaos 18, 3, p. 033125.
    • (2008) Chaos , vol.18 , Issue.3 , pp. 033125
    • Simpson, D.1    Meiss, J.2
  • 249
    • 67650757435 scopus 로고    scopus 로고
    • Shrinking point bifurcations of resonance tongues for piecewise-smooth, continuous maps
    • Simpson, D. and Meiss, J. (2009a). Shrinking point bifurcations of resonance tongues for piecewise-smooth, continuous maps. Nonlinearity 22, 5, pp. 1123-1144.
    • (2009) Nonlinearity , vol.22 , Issue.5 , pp. 1123-1144
    • Simpson, D.1    Meiss, J.2
  • 250
    • 70349633989 scopus 로고    scopus 로고
    • Simultaneous border-collision and period-doubling bifurcations
    • Simpson, D. and Meiss, J. (2009b). Simultaneous border-collision and period-doubling bifurcations. Chaos 19, 3, p. 033146.
    • (2009) Chaos , vol.19 , Issue.3 , pp. 033146
    • Simpson, D.1    Meiss, J.2
  • 252
    • 0019612168 scopus 로고
    • Chaos in a three-dimensional single loop feedback system with a piecewise linear feedback function
    • Sparrow, C. (1981). Chaos in a three-dimensional single loop feedback system with a piecewise linear feedback function. J. Math. Anal. Appl. 83, pp. 275-291.
    • (1981) J. Math. Anal. Appl , vol.83 , pp. 275-291
    • Sparrow, C.1
  • 253
    • 23844524438 scopus 로고    scopus 로고
    • Bistability and border-collision bifurcations for a family of unimodal piecewise smooth maps
    • Sushko, I., Agliari, A. and Gardini, L. (2005). Bistability and border-collision bifurcations for a family of unimodal piecewise smooth maps. Discrete Contin. Dyn. Syst. Ser. B 5, 3, pp. 881-897.
    • (2005) Discrete Contin. Dyn. Syst. Ser. B , vol.5 , Issue.3 , pp. 881-897
    • Sushko, I.1    Agliari, A.2    Gardini, L.3
  • 255
    • 45449105557 scopus 로고    scopus 로고
    • Center bifurcation for two-dimensional border-collision normal form
    • Sushko, I. and Gardini, L. (2008). Center bifurcation for two-dimensional border-collision normal form. Int. J. Bifurcation Chaos 18, 4, pp. 1029-1050.
    • (2008) Int. J. Bifurcation Chaos , vol.18 , Issue.4 , pp. 1029-1050
    • Sushko, I.1    Gardini, L.2
  • 256
    • 1142268100 scopus 로고    scopus 로고
    • Tongues of periodicity in a family of two-dimensional discontinuous maps of real Mäobius type
    • Sushko, I., Gardini, L. and Puu, T. (2004). Tongues of periodicity in a family of two-dimensional discontinuous maps of real Mäobius type. Chaos Solitons Fractals 21, pp. 403-412.
    • (2004) Chaos Solitons Fractals , vol.21 , pp. 403-412
    • Sushko, I.1    Gardini, L.2    Puu, T.3
  • 257
    • 46449116815 scopus 로고    scopus 로고
    • Invariant polygons in systems with grazing-sliding
    • Szalai, R. and Osinga, H. (2008). Invariant polygons in systems with grazing-sliding. Chaos 18, 2, p. 023121.
    • (2008) Chaos , vol.18 , Issue.2 , pp. 023121
    • Szalai, R.1    Osinga, H.2
  • 258
    • 1442286890 scopus 로고    scopus 로고
    • Bifurcation structures of period-adding phenomena in an ocean internal wave model
    • Tanaka, G., Murashige, S. and Aihara, K. (2003). Bifurcation structures of period-adding phenomena in an ocean internal wave model. Int. J. Bifurcation Chaos 13, 11, pp. 3409-3424.
    • (2003) Int. J. Bifurcation Chaos , vol.13 , Issue.11 , pp. 3409-3424
    • Tanaka, G.1    Murashige, S.2    Aihara, K.3
  • 259
    • 38248999679 scopus 로고
    • Generic bifurcation of sliding vector fields
    • Teixeira, M. (1993). Generic bifurcation of sliding vector fields. J. Math. Anal. Appl. 176, pp. 436-457.
    • (1993) J. Math. Anal. Appl , vol.176 , pp. 436-457
    • Teixeira, M.1
  • 261
    • 0042290616 scopus 로고
    • Towards the interpretation of the global bifurcation structure of the Lorenz system
    • Tomita, K. and Tsuda, I. (1980). Towards the interpretation of the global bifurcation structure of the Lorenz system. A simple one-dimensional model. Suppl. Prog. Theor. Phys. 69, pp. 185-199.
    • (1980) A simple one-dimensional model. Suppl. Prog. Theor. Phys , vol.69 , pp. 185-199
    • Tomita, K.1    Tsuda, I.2
  • 264
    • 24144464324 scopus 로고    scopus 로고
    • Symbolic analysis of bifurcation in switching power converters: Practical alternative viewpoint of border collision
    • Tse, C., Dai, D. and Ma, X. (2005). Symbolic analysis of bifurcation in switching power converters: Practical alternative viewpoint of border collision. Int. J. Bifurcation Chaos 15, 7, pp. 2263-2270.
    • (2005) Int. J. Bifurcation Chaos , vol.15 , Issue.7 , pp. 2263-2270
    • Tse, C.1    Dai, D.2    Ma, X.3
  • 270
    • 0001803202 scopus 로고
    • Stable synchrony oscillations in continuous cultures of Saccharomyces cerevisiae under glucose limitation
    • in B. Chance, E. Pye, T. Ghosh and B. Hess (eds.), (Academic Press, New York)
    • von Meyenburg, H. (1973). Stable synchrony oscillations in continuous cultures of Saccharomyces cerevisiae under glucose limitation. in B. Chance, E. Pye, T. Ghosh and B. Hess (eds.), Biological and Biochemical Oscillators. (Academic Press, New York), pp. 411-417.
    • (1973) Biological and Biochemical Oscillators , pp. 411-417
    • von Meyenburg, H.1
  • 271
    • 32044436353 scopus 로고    scopus 로고
    • Existence and bifurcation of canards in R3 in the case of a folded node
    • Wechselberger, M. (2005). Existence and bifurcation of canards in R3 in the case of a folded node. SIAM J. Appl. Dyn. Sys. 4, 1, pp. 101-139.
    • (2005) SIAM J. Appl. Dyn. Sys. , vol.4 , Issue.1 , pp. 101-139
    • Wechselberger, M.1
  • 274
    • 0003548726 scopus 로고    scopus 로고
    • Introduction to Applied Nonlinear Dynamical Systems and Chaos
    • Springer-Verlag, New York
    • Wiggins, S. (2003). Introduction to Applied Nonlinear Dynamical Systems and Chaos., Texts in Appl. Math., Vol. 2 (Springer-Verlag, New York).
    • (2003) Texts in Appl. Math , vol.2
    • Wiggins, S.1
  • 275
    • 0034257466 scopus 로고    scopus 로고
    • Piecewise-linear chaotic systems with a single equilibrium point
    • Yang, T. and Chua, L. (2000). Piecewise-linear chaotic systems with a single equilibrium point. Int. J. Bifurcation Chaos 10, 9, pp. 2015-2060.
    • (2000) Int. J. Bifurcation Chaos , vol.10 , Issue.9 , pp. 2015-2060
    • Yang, T.1    Chua, L.2
  • 276
    • 0042288649 scopus 로고
    • How the Arnol'd tongues become sausages in a piecewise linear circle map
    • Yang, W.-M. and Hao, B.-L. (1987). How the Arnol'd tongues become sausages in a piecewise linear circle map, Comm. Theoret. Phys. 8, pp. 1-15.
    • (1987) Comm. Theoret. Phys , vol.8 , pp. 1-15
    • Yang, W.-M.1    Hao, B.-L.2
  • 277
    • 23144464111 scopus 로고    scopus 로고
    • The genesis of period-adding bursting without bursting-chaos in the Chay model
    • Yang, Z., Lu, Q. and Li, L. (2006). The genesis of period-adding bursting without bursting-chaos in the Chay model. Chaos Solitons Fractals 27, pp. 689-697.
    • (2006) Chaos Solitons Fractals , vol.27 , pp. 689-697
    • Yang, Z.1    Lu, Q.2    Li, L.3
  • 279
    • 0036722112 scopus 로고    scopus 로고
    • Cell population models for bifurcation analysis and nonlinear control of continuous yeast bioreactors
    • Zhang, Y., Zamamiri, A., Henson, M. and Hjortso, M. (2002). Cell population models for bifurcation analysis and nonlinear control of continuous yeast bioreactors. J. Process Control 12, pp. 721-734.
    • (2002) J. Process Control , vol.12 , pp. 721-734
    • Zhang, Y.1    Zamamiri, A.2    Henson, M.3    Hjortso, M.4
  • 280
    • 30644460113 scopus 로고    scopus 로고
    • Unfolding degenerate grazing dynamics in impact actuators
    • Zhao, X. and Dankowicz, H. (2006). Unfolding degenerate grazing dynamics in impact actuators. Nonlinearity 19, 2, pp. 399-418.
    • (2006) Nonlinearity , vol.19 , Issue.2 , pp. 399-418
    • Zhao, X.1    Dankowicz, H.2
  • 281
    • 35148843633 scopus 로고    scopus 로고
    • Alternate pacing of border-collision period-doubling bifurcations
    • Zhao, X. and Schaeffer, D. (2007). Alternate pacing of border-collision period-doubling bifurcations. Nonlinear Dyn. 50, 3, pp. 733-742.
    • (2007) Nonlinear Dyn. , vol.50 , Issue.3 , pp. 733-742
    • Zhao, X.1    Schaeffer, D.2
  • 284
    • 32144442423 scopus 로고    scopus 로고
    • Birth of bilayered torus and torus breakdown in a piecewise-smooth dynamical system
    • Zhusubaliyev, Z. and Mosekilde, E. (2006a). Birth of bilayered torus and torus breakdown in a piecewise-smooth dynamical system. Phys. Lett. A 351, 3, pp. 167-174.
    • (2006) Phys. Lett. A , vol.351 , Issue.3 , pp. 167-174
    • Zhusubaliyev, Z.1    Mosekilde, E.2
  • 286
    • 39849101759 scopus 로고    scopus 로고
    • Direct transition from a stable equilibrium to quasiperiodicity in non-smooth systems
    • Zhusubaliyev, Z. and Mosekilde, E. (2008a). Direct transition from a stable equilibrium to quasiperiodicity in non-smooth systems. Phys. Lett. A 372, pp. 2237-2246.
    • (2008) Phys. Lett. A , vol.372 , pp. 2237-2246
    • Zhusubaliyev, Z.1    Mosekilde, E.2
  • 287
    • 42249113497 scopus 로고    scopus 로고
    • Equilibrium-torus bifurcation in nonsmooth systems
    • Zhusubaliyev, Z. and Mosekilde, E. (2008b). Equilibrium-torus bifurcation in nonsmooth systems. Phys. D 237, pp. 930-936.
    • (2008) Phys. D , vol.237 , pp. 930-936
    • Zhusubaliyev, Z.1    Mosekilde, E.2
  • 288
    • 40549085701 scopus 로고    scopus 로고
    • Transitions from phase-locked dynamics to chaos in a piecewise-linear map
    • Zhusubaliyev, Z., Mosekilde, E., De, S. and Banerjee, S. (2008). Transitions from phase-locked dynamics to chaos in a piecewise-linear map. Phys. Rev. E 77, p. 026206.
    • (2008) Phys. Rev. E , vol.77 , pp. 026206
    • Zhusubaliyev, Z.1    Mosekilde, E.2    De, S.3    Banerjee, S.4
  • 289
    • 33745711667 scopus 로고    scopus 로고
    • Border collision route to quasiperiodicity: Numerical investigation and experimental confirmation
    • Zhusubaliyev, Z., Mosekilde, E., Maity, S., Mohanan, S. and Banerjee, S. (2006). Border collision route to quasiperiodicity: Numerical investigation and experimental confirmation. Chaos 16, 2, p. 023122.
    • (2006) Chaos , vol.16 , Issue.2 , pp. 023122
    • Zhusubaliyev, Z.1    Mosekilde, E.2    Maity, S.3    Mohanan, S.4    Banerjee, S.5
  • 290
    • 0036643103 scopus 로고    scopus 로고
    • Border-collision bifurcations on a two-dimensional torus
    • Zhusubaliyev, Z., Soukhoterin, E. and Mosekilde, E. (2002). Border-collision bifurcations on a two-dimensional torus. Chaos Solitons Fractals 13, 9, pp. 1889-1915.
    • (2002) Chaos Solitons Fractals , vol.13 , Issue.9 , pp. 1889-1915
    • Zhusubaliyev, Z.1    Soukhoterin, E.2    Mosekilde, E.3
  • 291
    • 0042378939 scopus 로고    scopus 로고
    • Quasi-periodicity and border-collision bifurcations in a DC-DC converter with pulsewidth modulation
    • Zhusubaliyev, Z., Soukhoterin, E. and Mosekilde, E. (2003). Quasi-periodicity and border-collision bifurcations in a DC-DC converter with pulsewidth modulation. IEEE Trans. Circuits Systems I Fund. Theory Appl. 50, 8, pp. 1047-1057.
    • (2003) IEEE Trans. Circuits Systems I Fund. Theory Appl. , vol.50 , Issue.8 , pp. 1047-1057
    • Zhusubaliyev, Z.1    Soukhoterin, E.2    Mosekilde, E.3
  • 292
    • 33846080097 scopus 로고    scopus 로고
    • Quasiperiodicity and torus breakdown in a power electronic DC/DC converter
    • Zhusubaliyev, Z., Soukhoterin, E. and Mosekilde, E. (2007). Quasiperiodicity and torus breakdown in a power electronic DC/DC converter. Math. Comput. Simulation 73, pp. 364-377.
    • (2007) Math. Comput. Simulation , vol.73 , pp. 364-377
    • Zhusubaliyev, Z.1    Soukhoterin, E.2    Mosekilde, E.3
  • 293
    • 18444363345 scopus 로고    scopus 로고
    • Generalized Hopf bifurcation emanated from a corner for piecewise smooth planar systems
    • Zou, Y. and Käupper, T. (2005). Generalized Hopf bifurcation emanated from a corner for piecewise smooth planar systems, Non. Anal. 62, 1, pp. 1-17.
    • (2005) Non. Anal. , vol.62 , Issue.1 , pp. 1-17
    • Zou, Y.1    Käupper, T.2
  • 294
    • 84867977730 scopus 로고    scopus 로고
    • Generalized Hopf bifurcation for planar Filippov systems continuous at the origin
    • Zou, Y., Käupper, T. and Beyn, W.-J. (2006). Generalized Hopf bifurcation for planar Filippov systems continuous at the origin, J. Nonlinear Sci. 16, pp. 159-177.
    • (2006) J. Nonlinear Sci , vol.16 , pp. 159-177
    • Zou, Y.1    Käupper, T.2    Beyn, W.-J.3


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