메뉴 건너뛰기




Volumn 15, Issue 4, 2005, Pages 1267-1284

Period-doubling scenario without flip bifurcations in a one-dimensional map

Author keywords

Border collision; Kneading orbits; Period doubling; Piecewise smooth vector field

Indexed keywords

BIFURCATION (MATHEMATICS); DYNAMIC RESPONSE; FUNCTIONS; ORBITS; OSCILLATORS (ELECTRONIC); VECTORS;

EID: 22144444576     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127405012752     Document Type: Article
Times cited : (17)

References (58)
  • 1
    • 0000780796 scopus 로고    scopus 로고
    • Border collision bifurcation in two-dimensional piecewise smooth maps
    • Banerjee, S. & Grebogi, C. [1999] "Border collision bifurcation in two-dimensional piecewise smooth maps," Phys. Rev. E59, 4052-4061.
    • (1999) Phys. Rev. , vol.E59 , pp. 4052-4061
    • Banerjee, S.1    Grebogi, C.2
  • 2
    • 0000280845 scopus 로고    scopus 로고
    • Bifurcations from steady sliding to slip in boundary lubrication
    • Batista, A. & Carlson, J. M. [1998] "Bifurcations from steady sliding to slip in boundary lubrication," Phys. Rev. E57, 4986-4996.
    • (1998) Phys. Rev. , vol.E57 , pp. 4986-4996
    • Batista, A.1    Carlson, J.M.2
  • 5
    • 0000208406 scopus 로고
    • Grazing bifurcations in impact oscillators
    • Chin, W., Ott, E., Nusse, H. E. & Grebogi, C. [1994] "Grazing bifurcations in impact oscillators," Phys. Rev. E50, 4427-4444.
    • (1994) Phys. Rev. , vol.E50 , pp. 4427-4444
    • Chin, W.1    Ott, E.2    Nusse, H.E.3    Grebogi, C.4
  • 7
    • 0041822709 scopus 로고    scopus 로고
    • Grazing, skipping and sliding: Analysis of the nonsmooth dynamics of the dc/dc buck converter
    • di Bernardo, M., Budd, C. J. & Champneys, A. R. [1998a] "Grazing, skipping and sliding: Analysis of the nonsmooth dynamics of the dc/dc buck converter," Nonlinearity 11, 858-890.
    • (1998) Nonlinearity , vol.11 , pp. 858-890
    • Di Bernardo, M.1    Budd, C.J.2    Champneys, A.R.3
  • 8
  • 9
    • 22144472260 scopus 로고    scopus 로고
    • Sliding bifurcations in piecewise smooth dynamical systems
    • Catania, Italy
    • di Bernardo, M., Johansson, K. H. & Vasca, F. [2000] "Sliding bifurcations in piecewise smooth dynamical systems," in Proc. NDES00 Catania, Italy.
    • (2000) Proc. NDES00
    • Di Bernardo, M.1    Johansson, K.H.2    Vasca, F.3
  • 10
    • 0035877127 scopus 로고    scopus 로고
    • Corner collision implies border-collision bifurcation
    • di Bernardo, M., Budd, C. J. & Champneys, A. R. [2001a] "Corner collision implies border-collision bifurcation," Physica D154, 171-194.
    • (2001) Physica , vol.D154 , pp. 171-194
    • Di Bernardo, M.1    Budd, C.J.2    Champneys, A.R.3
  • 11
    • 0035911618 scopus 로고    scopus 로고
    • Grazing and border-collisions in piecewise-smooth systems: A unified analytical framework
    • di Bernardo, M., Budd, C. J. & Champneys, A. R. [2001b] "Grazing and border-collisions in piecewise-smooth systems: A unified analytical framework," Phys. Rev. Lett. 86, 2554-2556.
    • (2001) Phys. Rev. Lett. , vol.86 , pp. 2554-2556
    • Di Bernardo, M.1    Budd, C.J.2    Champneys, A.R.3
  • 12
    • 0035892830 scopus 로고    scopus 로고
    • Normal form maps for grazing bifurcations in n-dimensional piecewise-smooth dynamical systems
    • di Bernardo, M., Budd, C. J. & Champneys, A. R. [2001c] "Normal form maps for grazing bifurcations in n-dimensional piecewise-smooth dynamical systems," Physica D160, 222-254.
    • (2001) Physica , vol.D160 , pp. 222-254
    • Di Bernardo, M.1    Budd, C.J.2    Champneys, A.R.3
  • 14
    • 0038351322 scopus 로고    scopus 로고
    • Multi-attractor bifurcations: A source for unpredictability in piecewise smooth systems
    • Dutta, M., Nusse, H. E., Ott, E., Yorke, J. A. & Yuan, G. [1999] "Multi-attractor bifurcations: A source for unpredictability in piecewise smooth systems," Phys. Rev. Lett. 83, 4281-4284.
    • (1999) Phys. Rev. Lett. , vol.83 , pp. 4281-4284
    • Dutta, M.1    Nusse, H.E.2    Ott, E.3    Yorke, J.A.4    Yuan, G.5
  • 15
    • 0000863642 scopus 로고
    • Doubling of the oscillation period with C-bifurcations in piecewise-continuous systems
    • in Russian
    • Feigin, M. I. [1970] "Doubling of the oscillation period with C-bifurcations in piecewise-continuous systems," Prikl. Math. Mekh. 34, 861-869 (in Russian).
    • (1970) Prikl. Math. Mekh. , vol.34 , pp. 861-869
    • Feigin, M.I.1
  • 16
    • 0000516779 scopus 로고
    • On the generation of subharmonic modes in a piecewise-continuous system
    • in Russian
    • Feigin, M. I. [1975] "On the generation of subharmonic modes in a piecewise-continuous system," Prikl. Math. Mekh. 38, 810-818 (in Russian).
    • (1975) Prikl. Math. Mekh. , vol.38 , pp. 810-818
    • Feigin, M.I.1
  • 17
    • 0018210582 scopus 로고
    • On the structure of C-bifurcation boundaries of piecewise-continuous systems
    • in Russian
    • Feigin, M. I. [1978] "On the structure of C-bifurcation boundaries of piecewise-continuous systems," Prikl. Math. Mekh. 42, 820-829 (in Russian).
    • (1978) Prikl. Math. Mekh. , vol.42 , pp. 820-829
    • Feigin, M.I.1
  • 18
    • 0032159688 scopus 로고    scopus 로고
    • Basin bifurcation in quasiperiodically forced systems
    • Feudel, U., Witt, A., Lai, Y.-C. & Grebogi, C. [1998] "Basin bifurcation in quasiperiodically forced systems," Phys. Rev. E58, 3060-3066.
    • (1998) Phys. Rev. , vol.E58 , pp. 3060-3066
    • Feudel, U.1    Witt, A.2    Lai, Y.-C.3    Grebogi, C.4
  • 19
    • 0000501202 scopus 로고
    • Analytical determination of bifurcations in an impact oscillator
    • Foale, S. [1994] "Analytical determination of bifurcations in an impact oscillator," Proc. R. Soc. Lond. A347, 353-364.
    • (1994) Proc. R. Soc. Lond. , vol.A347 , pp. 353-364
    • Foale, S.1
  • 20
    • 0000793023 scopus 로고
    • New universal scenarios for the onset of chaos in Lorenz-type flows
    • Gambaudo, J.-M., Procaccia, I., Thomae, S. & Tresser, C. [1986] "New universal scenarios for the onset of chaos in Lorenz-type flows," Phys. Rev. Lett. 57, 925-928.
    • (1986) Phys. Rev. Lett. , vol.57 , pp. 925-928
    • Gambaudo, J.-M.1    Procaccia, I.2    Thomae, S.3    Tresser, C.4
  • 21
    • 51649168546 scopus 로고
    • Structural stability of Lorenz attractors
    • Guckenheimer, J. & Williams, R. F. [1979] "Structural stability of Lorenz attractors," Publ. Math. IHES 50, 307-320.
    • (1979) Publ. Math. IHES , vol.50 , pp. 307-320
    • Guckenheimer, J.1    Williams, R.F.2
  • 22
    • 0001338470 scopus 로고    scopus 로고
    • Dynamics of oscillators with impact and friction
    • Hinrichs, N., Oestreich, M. & Popp, K. [1997] "Dynamics of oscillators with impact and friction," Chaos Solit. Fract 8, 535-558.
    • (1997) Chaos Solit. Fract , vol.8 , pp. 535-558
    • Hinrichs, N.1    Oestreich, M.2    Popp, K.3
  • 23
    • 0035249490 scopus 로고    scopus 로고
    • Bifurcation behavior in parallel-connected buck converters
    • Iu, H. H. C. & Tse, C. K. [2001] "Bifurcation behavior in parallel-connected buck converters," Fundam. Th. Appl. 48, 233-240.
    • (2001) Fundam. Th. Appl. , vol.48 , pp. 233-240
    • Iu, H.H.C.1    Tse, C.K.2
  • 24
    • 35949022278 scopus 로고
    • Images of the critical points of nonlinear maps
    • Jensen, R. V. & Myers, C. R. [1985] "Images of the critical points of nonlinear maps," Phys. Rev. A32, 1222-1224.
    • (1985) Phys. Rev. , vol.A32 , pp. 1222-1224
    • Jensen, R.V.1    Myers, C.R.2
  • 25
    • 84944263887 scopus 로고    scopus 로고
    • On a novel class of bifurcations in hybrid dynamical systems
    • eds. di Bebedetto, M. & Sangiovanni-Vincentelli, A., LNCS
    • Kowalczyk, P. & di Bernardo, M. [2001] "On a novel class of bifurcations in hybrid dynamical systems," in Hybrid Systems: Computation and Control, eds. di Bebedetto, M. & Sangiovanni-Vincentelli, A., LNCS Vol. 2034 (Springer), pp. 361-374.
    • (2001) Hybrid Systems: Computation and Control , vol.2034 , Issue.SPRINGER , pp. 361-374
    • Kowalczyk, P.1    Di Bernardo, M.2
  • 26
    • 35648957325 scopus 로고
    • Scaling of Lyapunov exponents at nonsmooth bifurcations
    • Lamba, H. & Budd, C. J. [1994] "Scaling of Lyapunov exponents at nonsmooth bifurcations," Phys. Rev. E50, 84-90.
    • (1994) Phys. Rev. , vol.E50 , pp. 84-90
    • Lamba, H.1    Budd, C.J.2
  • 27
    • 0000241853 scopus 로고
    • Deterministic non-periodic flows
    • Lorenz, E. N. [1963] "Deterministic non-periodic flows," J. Atmos. Sci. 20, p. 130.
    • (1963) J. Atmos. Sci. , vol.20 , pp. 130
    • Lorenz, E.N.1
  • 30
    • 0347906198 scopus 로고    scopus 로고
    • Bifurcations of attracting cycles of piecewise linear interval maps
    • Maistrenko, Y. L., Maistrenko, V. L. & Vikul, S. I. [1996] "Bifurcations of attracting cycles of piecewise linear interval maps," J. Tech. Phys. 37, 367-370.
    • (1996) J. Tech. Phys. , vol.37 , pp. 367-370
    • Maistrenko, Y.L.1    Maistrenko, V.L.2    Vikul, S.I.3
  • 31
    • 0031673927 scopus 로고    scopus 로고
    • On period-adding sequences of attracting cycles in piecewise linear maps
    • Maistrenko, Y. L., Maistrenko, V. L. & Vikul, S. I. [1998] "On period-adding sequences of attracting cycles in piecewise linear maps," Chaos Solit. Fract. 9, 67-75.
    • (1998) Chaos Solit. Fract. , vol.9 , pp. 67-75
    • Maistrenko, Y.L.1    Maistrenko, V.L.2    Vikul, S.I.3
  • 32
    • 0015858113 scopus 로고
    • On finite limit sets for transformations on the unit interval
    • Metropolis, N., Stein, M. L. & Stein, P. R. [1973] "On finite limit sets for transformations on the unit interval," J. Comb. Th. A15, 25-44.
    • (1973) J. Comb. Th. , vol.A15 , pp. 25-44
    • Metropolis, N.1    Stein, M.L.2    Stein, P.R.3
  • 33
    • 0000848698 scopus 로고
    • On iterated maps of the interval
    • ed. Alexander, J. C., Lecture Notes in Mathematics
    • Milnor, J. & Thurston, W. [1987] "On iterated maps of the interval," in Dynamical Systems, ed. Alexander, J. C., Lecture Notes in Mathematics, Vol. 1342 (Springer), pp. 465-563.
    • (1987) Dynamical Systems , vol.1342 , Issue.SPRINGER , pp. 465-563
    • Milnor, J.1    Thurston, W.2
  • 34
    • 44949270133 scopus 로고
    • Periodic orbits for interval maps with sharp cusps
    • Misiurevicz, M. & Kawczyński, A. L. [1991] "Periodic orbits for interval maps with sharp cusps," Physica D52, 191-203.
    • (1991) Physica , vol.D52 , pp. 191-203
    • Misiurevicz, M.1    Kawczyński, A.L.2
  • 36
    • 0032156397 scopus 로고    scopus 로고
    • Existence of multiple attractors and the nature of bifurcations in a discontinuous logistic map
    • Nair, P. R. K. & Nandakumaran, V. M. [1998] "Existence of multiple attractors and the nature of bifurcations in a discontinuous logistic map," Pramana 51, 377-385.
    • (1998) Pramana , vol.51 , pp. 377-385
    • Nair, P.R.K.1    Nandakumaran, V.M.2
  • 37
    • 0026419524 scopus 로고
    • Non-periodic motion caused by grazing incidence in an impact oscillator
    • Nordmark, A. B. [1991] "Non-periodic motion caused by grazing incidence in an impact oscillator," J. Sound Vib. 145, 279-297.
    • (1991) J. Sound Vib. , vol.145 , pp. 279-297
    • Nordmark, A.B.1
  • 38
    • 4244118801 scopus 로고    scopus 로고
    • Universal limit mapping in grazing bifurcations
    • Nordmark, A. B. [1997] "Universal limit mapping in grazing bifurcations," Phys. Rev. E55, 266-270.
    • (1997) Phys. Rev. , vol.E55 , pp. 266-270
    • Nordmark, A.B.1
  • 39
    • 44049121950 scopus 로고
    • Border-collision bifurcations including 'period two to period three' bifurcation for piecewise smooth systems
    • Nusse, H. E. & Yorke, J. A. [1992] "Border-collision bifurcations including 'period two to period three' bifurcation for piecewise smooth systems," Physica D57, 39-57.
    • (1992) Physica , vol.D57 , pp. 39-57
    • Nusse, H.E.1    Yorke, J.A.2
  • 40
    • 0001050846 scopus 로고
    • Border-collision bifurcations: An explanation for observed bifurcation phenomena
    • Nusse, H. E., Ott, E. & Yorke, J. A. [1994] "Border-collision bifurcations: An explanation for observed bifurcation phenomena," Phys. Rev. E49, 1073-1076.
    • (1994) Phys. Rev. , vol.E49 , pp. 1073-1076
    • Nusse, H.E.1    Ott, E.2    Yorke, J.A.3
  • 41
    • 4344639901 scopus 로고
    • Border-collision bifurcations for piecewise smooth one-dimensional map
    • Nusse, H. E. & Yorke, J. A. [1995] "Border-collision bifurcations for piecewise smooth one-dimensional map," Int. J. Bifurcation and Chaos 5, 189-207.
    • (1995) Int. J. Bifurcation and Chaos , vol.5 , pp. 189-207
    • Nusse, H.E.1    Yorke, J.A.2
  • 42
    • 0036925763 scopus 로고    scopus 로고
    • Border collision bifurcations at the change of state-space dimension
    • Parui, S. & Banerjee, S. [2002] "Border collision bifurcations at the change of state-space dimension," Chaos 12, 1054-1069.
    • (2002) Chaos , vol.12 , pp. 1054-1069
    • Parui, S.1    Banerjee, S.2
  • 43
    • 0242696105 scopus 로고    scopus 로고
    • Bifurcations due to transition from continuous conduction mode to discontinuous conduction mode in the boost converter
    • Parui, S. & Banerjee, S. [2003] "Bifurcations due to transition from continuous conduction mode to discontinuous conduction mode in the boost converter," IEEE Trans. Circuits Syst.-I, 1464-1469.
    • (2003) IEEE Trans. Circuits Syst.-I , pp. 1464-1469
    • Parui, S.1    Banerjee, S.2
  • 44
    • 0000078121 scopus 로고
    • Mechanism for global features of chaos in a driven nonlinear oscillator
    • Perez, J. M. [1985] "Mechanism for global features of chaos in a driven nonlinear oscillator," Phys. Rev. A32, 2513-2516.
    • (1985) Phys. Rev. , vol.A32 , pp. 2513-2516
    • Perez, J.M.1
  • 45
    • 0000792701 scopus 로고    scopus 로고
    • Bifurcations and transition phenomena in an impact oscillator
    • Peterka, F. [1996] "Bifurcations and transition phenomena in an impact oscillator," Chaos Solit. Fract. 7, 1635-1647.
    • (1996) Chaos Solit. Fract. , vol.7 , pp. 1635-1647
    • Peterka, F.1
  • 46
    • 0000651439 scopus 로고
    • First-return maps as a unified renormalization scheme for dynamical systems
    • Procaccia, I., Thomae, S. & Tresser, C. [1987] "First-return maps as a unified renormalization scheme for dynamical systems," Phys. Rev. A35, 1884-1900.
    • (1987) Phys. Rev. , vol.A35 , pp. 1884-1900
    • Procaccia, I.1    Thomae, S.2    Tresser, C.3
  • 47
    • 0027678542 scopus 로고
    • Chaos in some 1-d discontinuous maps that appear in the analysis of electrical circuits
    • Sharkovsky, A. N. & Chua, L. O. [1993] "Chaos in some 1-d discontinuous maps that appear in the analysis of electrical circuits," IEEE Trans. Circuits Syst.-I 40, 722-731.
    • (1993) IEEE Trans. Circuits Syst.-I , vol.40 , pp. 722-731
    • Sharkovsky, A.N.1    Chua, L.O.2
  • 49
    • 0036537746 scopus 로고    scopus 로고
    • Analysis of border-collision bifurcations in a flow model of a switching system
    • Tanaka, H. & Ushio, T. [2002] "Analysis of border-collision bifurcations in a flow model of a switching system," IEICE Trans. Fund. Electro. Commun. Comput. Sci. E85-A, 734-739.
    • (2002) IEICE Trans. Fund. Electro. Commun. Comput. Sci. , vol.E85-A , pp. 734-739
    • Tanaka, H.1    Ushio, T.2
  • 50
    • 0011007151 scopus 로고    scopus 로고
    • An experimental impact oscillator
    • Todd, M. D. & Virgin, L. N. [1997] "An experimental impact oscillator," Chaos Solit. Fract. 8, 699-714.
    • (1997) Chaos Solit. Fract. , vol.8 , pp. 699-714
    • Todd, M.D.1    Virgin, L.N.2
  • 52
    • 0032119909 scopus 로고    scopus 로고
    • Border-collision bifurcations in the buck converter
    • Yuan, G., Banerjee, S., Ott, E. & Yorke, J. A. [1998] "Border-collision bifurcations in the buck converter," Fundam. Th. Appl. 45, 707-716.
    • (1998) Fundam. Th. Appl. , vol.45 , pp. 707-716
    • Yuan, G.1    Banerjee, S.2    Ott, E.3    Yorke, J.A.4
  • 53
    • 0012711550 scopus 로고
    • Symbolic dynamics for the gap map
    • Zheng, W.-M. [1989] "Symbolic dynamics for the gap map," Phys. Rev. A39, 6608-6610.
    • (1989) Phys. Rev. , vol.A39 , pp. 6608-6610
    • Zheng, W.-M.1
  • 54
    • 0001709060 scopus 로고
    • Applied symbolic dynamics for the Lorenz-like map
    • Zheng, W.-M. [1990] "Applied symbolic dynamics for the Lorenz-like map," Phys. Rev. A42, 2076-2080.
    • (1990) Phys. Rev. , vol.A42 , pp. 2076-2080
    • Zheng, W.-M.1
  • 55
    • 0035652473 scopus 로고    scopus 로고
    • Border-collision bifurcations and chaotic oscillations in a piecewise smooth dynamical system
    • Zhusubaliyev, Z., Soukhoterin, E. & Mosekilde, E. [2001] "Border-collision bifurcations and chaotic oscillations in a piecewise smooth dynamical system," Int. J. Bifurcation and Chaos 11, 2977-3001.
    • (2001) Int. J. Bifurcation and Chaos , vol.11 , pp. 2977-3001
    • Zhusubaliyev, Z.1    Soukhoterin, E.2    Mosekilde, E.3
  • 56
  • 58
    • 0042378939 scopus 로고    scopus 로고
    • Quasi-periodicity and border-collision bifurcations in a dc-dc converter with pulsewidth modulation
    • Zhusubaliyev, Z., Soukhoterin, E. & Mosekilde, E. [2003] "Quasi-periodicity and border-collision bifurcations in a dc-dc converter with pulsewidth modulation," IEEE Trans. Circuits Syst.-I 50, 1047-1057.
    • (2003) IEEE Trans. Circuits Syst.-I , vol.50 , pp. 1047-1057
    • Zhusubaliyev, Z.1    Soukhoterin, E.2    Mosekilde, E.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.