메뉴 건너뛰기




Volumn , Issue , 2006, Pages 1-363

New Methods For Chaotic Dynamics

Author keywords

[No Author keywords available]

Indexed keywords


EID: 84994244165     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1142/6117     Document Type: Book
Times cited : (42)

References (147)
  • 2
    • 0038818452 scopus 로고    scopus 로고
    • Control of chaos: Methods and applications. I
    • in Russian
    • Andrievskii, B.R., Fradkov A.L. (2003). Control of chaos: methods and applications. I. Methods. Aut. Rem. Control, 64, 5, pp. 673-713 (in Russian).
    • (2003) Methods. Aut. Rem. Control , vol.64 , Issue.5 , pp. 673-713
    • Andrievskii, B.R.1    Fradkov, A.L.2
  • 6
    • 0003536096 scopus 로고    scopus 로고
    • Non-linear dynamics of chaotic and stochastic systems
    • Edited by V.S. Anishchenko. - Saratov: Published by Saratov University, in Russian
    • Anishchenko, V.S., Vadivasova, T.A., Astakhov, V.V. (1999). Non-linear dynamics of chaotic and stochastic systems. Fundamental basis and selected problems. Edited by V.S. Anishchenko. - Saratov: Published by Saratov University, 368p. (in Russian).
    • (1999) Fundamental basis and selected problems , pp. 368
    • Anishchenko, V.S.1    Vadivasova, T.A.2    Astakhov, V.V.3
  • 7
    • 52549119044 scopus 로고
    • Ergodic properties of geodesic flows on closed Riemannian manifolds of negative curvature
    • English translation in Soviet Math. Dokl. 4
    • Anosov, D.V. (1963). Ergodic properties of geodesic flows on closed Riemannian manifolds of negative curvature. Dokl. Akad. Nauk USSR, 151, pp. 1250-1252. English translation in Soviet Math. Dokl. 4, pp. 1153-1156.
    • (1963) Dokl. Akad. Nauk USSR , vol.151
    • Anosov, D.V.1
  • 12
    • 0004279024 scopus 로고
    • Third edition, extended. - Moscow: Nauka, in Russian
    • Arnold, V.I. (1990). Catastrophe theory. Third edition, extended. - Moscow: Nauka, 128p. (in Russian)
    • (1990) Catastrophe theory , pp. 128
    • Arnold, V.I.1
  • 15
    • 0001976684 scopus 로고    scopus 로고
    • Inverting chaos: Extracting system parameters from experimental data
    • Baker, C.L., Collub J.P. and Blackburn J.A. (1996). Inverting chaos: extracting system parameters from experimental data. Chaos, 4, pp. 528-533.
    • (1996) Chaos , vol.4 , pp. 528-533
    • Baker, C.L.1    Collub, J.P.2    Blackburn, J.A.3
  • 19
    • 0001581120 scopus 로고
    • Modelling and synchronizing chaotic systems from time-series data
    • Brown, R., Rulkov, N.F. and Tracy, E.R. (1994). Modelling and synchronizing chaotic systems from time-series data. Phys. Rev. E, 49, pp. 3784-3800.
    • (1994) Phys. Rev. E , vol.49 , pp. 3784-3800
    • Brown, R.1    Rulkov, N.F.2    Tracy, E.R.3
  • 21
    • 0030540448 scopus 로고    scopus 로고
    • Lorenz equations. Part I: Existence and nonexistence of homo-clinic orbits
    • Chen, X. (1996). Lorenz equations. Part I: Existence and nonexistence of homo-clinic orbits. SI AM J. Math. Anal, 27, 4, pp. 1057-1069.
    • (1996) SI AM J. Math. Anal , vol.27 , Issue.4 , pp. 1057-1069
    • Chen, X.1
  • 23
    • 85129026035 scopus 로고
    • Edited by Madan, R.N. World scientific, Singapore
    • Chua’s circuit: a paradigm for chaos. (1993). Edited by Madan, R.N. World scientific, Singapore.
    • (1993)
  • 25
    • 0000852213 scopus 로고
    • Universal properties of maps of an interval
    • Collet, P., Eckmann, J.P. and Lanford, O.E. (1980). Universal properties of maps of an interval. Comm. Math. Phys. 76, pp. 211-254.
    • (1980) Comm. Math. Phys. , vol.76 , pp. 211-254
    • Collet, P.1    Eckmann, J.P.2    Lanford, O.E.3
  • 26
    • 0014839691 scopus 로고
    • The Rikitaki two-disc dynamo system
    • Cook, A.E. and Roberts, P.H. (1970). The Rikitaki two-disc dynamo system. Proc. Camb. Phil. Soc, 68, pp. 547-569.
    • (1970) Proc. Camb. Phil. Soc , vol.68 , pp. 547-569
    • Cook, A.E.1    Roberts, P.H.2
  • 27
    • 0003254098 scopus 로고
    • Stability of solutions of differential equations in Banach space
    • translated from Russian
    • Daletskii, Y.L. and Krein, M.G. (1974). Stability of solutions of differential equations in Banach space. Amer. Math. Soc. 534p. (translated from Russian).
    • (1974) Amer. Math. Soc. , pp. 534
    • Daletskii, Y.L.1    Krein, M.G.2
  • 28
    • 0035568585 scopus 로고    scopus 로고
    • Regular dynamics and diffusion chaos in the Brusselator model
    • Dernov, A.V. (2001a). Regular dynamics and diffusion chaos in the Brusselator model. Differential equations, 37, 11, pp. 1631-1633.
    • (2001) Differential equations , vol.37 , Issue.11 , pp. 1631-1633
    • Dernov, A.V.1
  • 29
    • 85129105465 scopus 로고    scopus 로고
    • Stabilization of unstable periodic orbits of one-dimensional chaotic mappings
    • Eds. S.V. Emelyanov and S.K. Korovin. - Moscow: Fizmatlit, in Russian
    • Dernov, A.V. (2001b). Stabilization of unstable periodic orbits of one-dimensional chaotic mappings. Nonlinear Dynamics and Control, 1, Eds. S.V. Emelyanov and S.K. Korovin. - Moscow: Fizmatlit, pp. 247-252 (in Russian).
    • (2001) Nonlinear Dynamics and Control , vol.1 , pp. 247-252
    • Dernov, A.V.1
  • 30
    • 56749148893 scopus 로고    scopus 로고
    • Diffusion of the capital and demand in the model of self-developing market economy
    • Eds. S.V. Emelyanov, S.K. Korovin. - Moscow: Fizmatlit, in Russian
    • Dernov, A.V. (2002a). Diffusion of the capital and demand in the model of self-developing market economy. Nonlinear Dynamics and Control, 2, Eds. S.V. Emelyanov, S.K. Korovin. - Moscow: Fizmatlit, pp. 233-242 (in Russian).
    • (2002) Nonlinear Dynamics and Control , vol.2 , pp. 233-242
    • Dernov, A.V.1
  • 31
    • 85129053069 scopus 로고    scopus 로고
    • On new approaches to a problem of chaos control
    • in Russian
    • Dernov, A.V. (2002b). On new approaches to a problem of chaos control. Proc. of Moscow State University, 1, p. 31 (in Russian).
    • (2002) Proc. of Moscow State University , vol.1 , pp. 31
    • Dernov, A.V.1
  • 32
    • 32144438186 scopus 로고    scopus 로고
    • Transition to chaos in a nonclassical reaction-diffusion system
    • Dernov, A.V. and Magnitskii, N.A. (2005). Transition to chaos in a nonclassical reaction-diffusion system. Differential equations, 41, 12, pp. 1751-1756.
    • (2005) Differential equations , vol.41 , Issue.12 , pp. 1751-1756
    • Dernov, A.V.1    Magnitskii, N.A.2
  • 33
    • 35949018382 scopus 로고
    • Ergodic theory of chaos and strange at-tractors
    • Eckmann, J.P. and Ruelle, D. (1985). Ergodic theory of chaos and strange at-tractors. Rev. Mod. Phys., 57, 3, pp. 617-656.
    • (1985) Rev. Mod. Phys. , vol.57 , Issue.3 , pp. 617-656
    • Eckmann, J.P.1    Ruelle, D.2
  • 35
    • 0001816458 scopus 로고
    • Quantitative universality for a class of nonlinear transformations
    • Feigenbaum, M.J. (1978). Quantitative universality for a class of nonlinear transformations. J. Stat. Phys., 19, pp. 25-52.
    • (1978) J. Stat. Phys. , vol.19 , pp. 25-52
    • Feigenbaum, M.J.1
  • 36
    • 0002709930 scopus 로고
    • Universal behavior in nonlinear systems
    • Feigenbaum, M.J. (1980). Universal behavior in nonlinear systems. Los Alamos. Sei, 1, 1, pp. 4-27.
    • (1980) Los Alamos. Sei , vol.1 , Issue.1 , pp. 4-27
    • Feigenbaum, M.J.1
  • 37
    • 34548078485 scopus 로고
    • Dispersive instabilities in nonlinear systems: The real and complex Lorenz equations
    • Ed. H. Haken, Springer Verlag, New York
    • Gibbon, J.D. (1981). Dispersive instabilities in nonlinear systems: the real and complex Lorenz equations. Proc. Int. Symp. on Synergetics. Ed. H. Haken, pp. 92-101. Springer Verlag, New York.
    • (1981) Proc. Int. Symp. on Synergetics. , pp. 92-101
    • Gibbon, J.D.1
  • 39
    • 38849112091 scopus 로고    scopus 로고
    • Analytical conditions of existence of homoclinic loop in the Chua circuits
    • Eds. S.V. Emelyanov, S.K. Korovin. - Moscow: Fizmatlit, in Russian
    • Gribov, A.F. and Krischenko, A.P. (2001). Analytical conditions of existence of homoclinic loop in the Chua circuits. Nonlinear Dynamics and Control, 1, Eds. S.V. Emelyanov, S.K. Korovin. - Moscow: Fizmatlit, pp. 263-268 (in Russian).
    • (2001) Nonlinear Dynamics and Control , vol.1 , pp. 263-268
    • Gribov, A.F.1    Krischenko, A.P.2
  • 40
    • 0003372424 scopus 로고
    • Strange, strange attractor
    • Eds. J.E. Marsden and M. McCracken. Springer Verlag, New York
    • Guckenheimer, J.A. (1976). Strange, strange attractor. In The Hopf Bifurcation and Its Applications, Eds. J.E. Marsden and M. McCracken. Springer Verlag, New York.
    • (1976) The Hopf Bifurcation and Its Applications
    • Guckenheimer, J.A.1
  • 42
    • 51649168546 scopus 로고
    • Structural stability of Lorenz at-tractors
    • Guckenheimer, J. and Williams, R.F. (1979). Structural stability of Lorenz at-tractors. Puhl. Math. IHES, 50, pp. 59-72.
    • (1979) Puhl. Math. IHES , vol.50 , pp. 59-72
    • Guckenheimer, J.1    Williams, R.F.2
  • 48
    • 0002591468 scopus 로고
    • A two-dimensional mapping with a strange attractor
    • Henon, M. (1976). A two-dimensional mapping with a strange attractor. Comm. Math. Phys., 50, p. 69.
    • (1976) Comm. Math. Phys. , vol.50 , pp. 69
    • Henon, M.1
  • 51
    • 0002053804 scopus 로고
    • Absolutely continuous measures for one parameter families of one-dimensional maps
    • Jakobson, M.V. (1981). Absolutely continuous measures for one parameter families of one-dimensional maps. Comm. Math. Phys., 81, pp. 39-88.
    • (1981) Comm. Math. Phys. , vol.81 , pp. 39-88
    • Jakobson, M.V.1
  • 52
    • 0035565971 scopus 로고    scopus 로고
    • Search and stabilization of unstable saddle cycles in Lorenz system
    • Kaloshin, D.A. (2001). Search and stabilization of unstable saddle cycles in Lorenz system. Differential equations, 37, 11, pp. 1636-1639.
    • (2001) Differential equations , vol.37 , Issue.11 , pp. 1636-1639
    • Kaloshin, D.A.1
  • 53
    • 3543112554 scopus 로고    scopus 로고
    • On construction of bifurcation surface of homoclinic butterfly in the Lorenz system
    • Kaloshin, D.A. (2003). On construction of bifurcation surface of homoclinic butterfly in the Lorenz system. Differential equations, 39, 11, pp. 1648-1650.
    • (2003) Differential equations , vol.39 , Issue.11 , pp. 1648-1650
    • Kaloshin, D.A.1
  • 54
    • 30344475928 scopus 로고    scopus 로고
    • On some features of transition to chaos in the system of Lorenz equations
    • Eds. S.V. Emelyanov, S.K. Korovin. - Moscow: Fizmatlit, in Russian
    • Kaloshin, D.A., Magnitskii, N.A. and Sidorov, S.V. (2003). On some features of transition to chaos in the system of Lorenz equations. Nonlinear Dynamics and Control, 3, Eds. S.V. Emelyanov, S.K. Korovin. - Moscow: Fizmatlit, pp. 99-106 (in Russian).
    • (2003) Nonlinear Dynamics and Control , vol.3 , pp. 99-106
    • Kaloshin, D.A.1    Magnitskii, N.A.2    Sidorov, S.V.3
  • 55
    • 0000093381 scopus 로고
    • Global bifurcation analysis of the double scroll circuit
    • Komuro, M., Matsumoto, T., Chua, L.O. et al. (1991). Global bifurcation analysis of the double scroll circuit. Intern. J. Bifurcation and chaos, 1, 1, pp. 139-182.
    • (1991) Intern. J. Bifurcation and chaos , vol.1 , Issue.1 , pp. 139-182
    • Komuro, M.1    Matsumoto, T.2    Chua, L.O.3
  • 56
    • 52649167332 scopus 로고    scopus 로고
    • Stabilization of unstable stationary points in the equations with delay argument
    • Knyazev, E.A., Magnitskii, N.A. and Sidorov, S.V. (1999). Stabilization of unstable stationary points in the equations with delay argument. Nonlinear dynamics. Trans. ISA RAS. - Moscow: Editorial URSS, pp. 133-141.
    • (1999) Nonlinear dynamics. Trans. ISA RAS. , pp. 133-141
    • Knyazev, E.A.1    Magnitskii, N.A.2    Sidorov, S.V.3
  • 57
    • 0000944744 scopus 로고
    • On the formation of dissipative structures in reaction-diffusion systems
    • Kuramoto, Y. and Tsuzuki, T. (1975). On the formation of dissipative structures in reaction-diffusion systems. Progr. Theor. Phys., 54, 3, pp. 687-699.
    • (1975) Progr. Theor. Phys. , vol.54 , Issue.3 , pp. 687-699
    • Kuramoto, Y.1    Tsuzuki, T.2
  • 58
    • 0141885533 scopus 로고    scopus 로고
    • Moscow: Fizmatlit, in Russian
    • Kuznetzov, S.P. (2001). Dynamical chaos. - Moscow: Fizmatlit, 296p. (in Russian).
    • (2001) Dynamical chaos , pp. 296
    • Kuznetzov, S.P.1
  • 60
    • 36849102494 scopus 로고
    • Symmetry-breaking instabilities in dissipative systems
    • Lefever, R. and Prigogine, I. (1968). Symmetry-breaking instabilities in dissipative systems. J. Chem. Phys., 48, pp. 1695-1700.
    • (1968) J. Chem. Phys. , vol.48 , pp. 1695-1700
    • Lefever, R.1    Prigogine, I.2
  • 61
    • 84868132706 scopus 로고
    • An estimate of the bifurcation parameters of the separatrix loop of a saddle point of the Lorenz system
    • Leonov, G.A. (1988). An estimate of the bifurcation parameters of the separatrix loop of a saddle point of the Lorenz system. Differential equations, 24, 6, pp. 634-638.
    • (1988) Differential equations , vol.24 , Issue.6 , pp. 634-638
    • Leonov, G.A.1
  • 62
    • 0000100336 scopus 로고
    • Period three implies chaos
    • Li, T.Y. and Yorke, J.A. (1975). Period three implies chaos. Amer. Math. Monthly, 82, 10, pp. 982-985.
    • (1975) Amer. Math. Monthly , vol.82 , Issue.10 , pp. 982-985
    • Li, T.Y.1    Yorke, J.A.2
  • 63
    • 0000241853 scopus 로고
    • Deterministic nonperiodic flow
    • Lorenz, E.N. (1963). Deterministic nonperiodic flow. J. Atmos. Sci., 20, pp. 130-141.
    • (1963) J. Atmos. Sci. , vol.20 , pp. 130-141
    • Lorenz, E.N.1
  • 64
    • 0347371564 scopus 로고    scopus 로고
    • Chaos and control in dynamical systems
    • Eds. S.V. Emelyanov, S.K. Korovin. - Moscow: Fizmatlit, in Russian
    • Loskutov, A.Y. (2001). Chaos and control in dynamical systems. Nonlinear Dynamics and Control, 1, Eds. S.V. Emelyanov, S.K. Korovin. - Moscow: Fizmatlit, pp. 163-216 (in Russian).
    • (2001) Nonlinear Dynamics and Control , vol.1 , pp. 163-216
    • Loskutov, A.Y.1
  • 66
    • 0000591151 scopus 로고
    • Power low decay of correlation in a billiard problem
    • Machta, J. (1983). Power low decay of correlation in a billiard problem. J. of Stat. Phys., 32, 3, pp. 555-564.
    • (1983) J. of Stat. Phys. , vol.32 , Issue.3 , pp. 555-564
    • Machta, J.1
  • 67
    • 0017714604 scopus 로고
    • Oscillations and chaos in physiological control systems
    • Mackey, M. and Glass, L. (1977). Oscillations and chaos in physiological control systems. Science, 197, pp. 287-289.
    • (1977) Science , vol.197 , pp. 287-289
    • Mackey, M.1    Glass, L.2
  • 68
    • 77958450912 scopus 로고
    • Mathematical model of self-developing market economy
    • in Russian
    • Magnitskii, N.A. (1991). Mathematical model of self-developing market economy. Trans. ISR AS USSR, pp. 16-22. (in Russian).
    • (1991) Trans. ISR AS USSR , pp. 16-22
    • Magnitskii, N.A.1
  • 70
    • 0039406803 scopus 로고
    • Hopf bifurcation in the Rossler system
    • Magnitskii, N.A. (1995). Hopf bifurcation in the Rossler system. Differential equations, 31, 3, pp. 538-541.
    • (1995) Differential equations , vol.31 , Issue.3 , pp. 538-541
    • Magnitskii, N.A.1
  • 71
    • 0040592034 scopus 로고    scopus 로고
    • On stabilization of fixed points of chaotic mappings
    • Magnitskii, N.A. (1996). On stabilization of fixed points of chaotic mappings. Dokl. Akad. Nauk USSR, 351, 2, pp. 175-177.
    • (1996) Dokl. Akad. Nauk USSR , vol.351 , Issue.2 , pp. 175-177
    • Magnitskii, N.A.1
  • 72
    • 27144560375 scopus 로고    scopus 로고
    • On stabilization of fixed points of chaotic dynamical systems
    • Magnitskii, N.A. (1997a). On stabilization of fixed points of chaotic dynamical systems. Dokl. Akad. Nauk USSR, 352, 5, pp. 610-612.
    • (1997) Dokl. Akad. Nauk USSR , vol.352 , Issue.5 , pp. 610-612
    • Magnitskii, N.A.1
  • 73
    • 27144520680 scopus 로고    scopus 로고
    • On stabilization of unstable cycles of chaotic mappings
    • Magnitskii, N.A. (1997b). On stabilization of unstable cycles of chaotic mappings. Dokl. Akad. Nauk USSR, 355, 6, pp. 747-749.
    • (1997) Dokl. Akad. Nauk USSR , vol.355 , Issue.6 , pp. 747-749
    • Magnitskii, N.A.1
  • 74
    • 0031188946 scopus 로고    scopus 로고
    • Stabilization of unstable periodic orbits of chaotic maps
    • 1997
    • Magnitskii, N.A. (1997c). Stabilization of unstable periodic orbits of chaotic maps. Computers Math. Applic, 34, 2-4, 1997, pp. 369-372.
    • (1997) Computers Math. Applic , vol.34 , Issue.2-4 , pp. 369-372
    • Magnitskii, N.A.1
  • 75
    • 30344448981 scopus 로고    scopus 로고
    • On nature of chaotic attractors
    • Eds. S.V. Emelyanov, S.K. Korovin. - Moscow: Fizmatlit, in Russian
    • Magnitskii, N.A. (2004). On nature of chaotic attractors. Nonlinear Dynamics and Control, 4, Eds. S.V. Emelyanov, S.K. Korovin. - Moscow: Fizmatlit, pp. 37-58 (in Russian).
    • (2004) Nonlinear Dynamics and Control , vol.4 , pp. 37-58
    • Magnitskii, N.A.1
  • 76
    • 33846128344 scopus 로고    scopus 로고
    • On singular attractors of dissipative systems of nonlinear ordinary differential equations
    • Univ. Technol., Eindhoven
    • Magnitskii, N.A. (2005). On singular attractors of dissipative systems of nonlinear ordinary differential equations. Proc. of ENOC-2005 Int. Conf, Univ. Technol., Eindhoven, pp. 1285-1294.
    • (2005) Proc. of ENOC-2005 Int. Conf , pp. 1285-1294
    • Magnitskii, N.A.1
  • 77
    • 22644449444 scopus 로고    scopus 로고
    • Control of chaos in nonlinear dynamical systems
    • in Russian
    • Magnitskii, N.A. and Sidorov, S.V. (1998). Control of chaos in nonlinear dynamical systems. Differential equations, 34, 11, pp. 1051-1509 (in Russian).
    • (1998) Differential equations , vol.34 , Issue.11 , pp. 1051-1509
    • Magnitskii, N.A.1    Sidorov, S.V.2
  • 78
    • 27144502793 scopus 로고    scopus 로고
    • Some approaches to the control problem for diffusion chaos
    • Magnitskii, N.A. and Sidorov, S.V. (1999). Some approaches to the control problem for diffusion chaos. Differential equations, 35, 5, pp. 669-674.
    • (1999) Differential equations , vol.35 , Issue.5 , pp. 669-674
    • Magnitskii, N.A.1    Sidorov, S.V.2
  • 79
    • 30744437670 scopus 로고    scopus 로고
    • Stabilization of unstable periodic solutions of delay equations
    • Magnitskii, N.A. and Sidorov, S.V. (2000). Stabilization of unstable periodic solutions of delay equations. Differential equations, 36, 11, pp. 1634-1638.
    • (2000) Differential equations , vol.36 , Issue.11 , pp. 1634-1638
    • Magnitskii, N.A.1    Sidorov, S.V.2
  • 81
    • 85129055408 scopus 로고    scopus 로고
    • Localization and stabilization of unstable solutions of chaotic dynamical systems
    • Eds. S.V. Emelyanov, S.K. Korovin. - Moscow: Fizmatlit, in Russian
    • Magnitskii, N.A. and Sidorov, S.V. (2001b). Localization and stabilization of unstable solutions of chaotic dynamical systems. Nonlinear Dynamics and Control, 1, Eds. S.V. Emelyanov, S.K. Korovin. - Moscow: Fizmatlit, pp. 217-246 (in Russian).
    • (2001) Nonlinear Dynamics and Control , vol.1 , pp. 217-246
    • Magnitskii, N.A.1    Sidorov, S.V.2
  • 82
    • 0035565844 scopus 로고    scopus 로고
    • A new view of the Lorenz attractor
    • Magnitskii, N.A. and Sidorov, S.V. (2001c). A new view of the Lorenz attractor. Differential equations, 37, 11, pp. 1568-1579.
    • (2001) Differential equations , vol.37 , Issue.11 , pp. 1568-1579
    • Magnitskii, N.A.1    Sidorov, S.V.2
  • 83
    • 0038175526 scopus 로고    scopus 로고
    • Transition to chaos in nonlinear dynamical systems through a subharmonic cascade of bifurcations of two-dimensional tori
    • Magnitskii, N.A. and Sidorov, S.V. (2002). Transition to chaos in nonlinear dynamical systems through a subharmonic cascade of bifurcations of two-dimensional tori. Differential equations, 38, 12, pp. 1703-1708.
    • (2002) Differential equations , vol.38 , Issue.12 , pp. 1703-1708
    • Magnitskii, N.A.1    Sidorov, S.V.2
  • 84
    • 38849204448 scopus 로고    scopus 로고
    • On scenarios of transition to chaos in nonlinear dynamical systems described by ordinary differential equations
    • Eds. S.V. Emelyanov, S.K. Korovin. - Moscow: Fizmatlit, in Russian
    • Magnitskii, N.A. and Sidorov, S.V. (2003a). On scenarios of transition to chaos in nonlinear dynamical systems described by ordinary differential equations. Nonlinear Dynamics and Control, 3, Eds. S.V. Emelyanov, S.K. Korovin. - Moscow: Fizmatlit, pp. 73-98 (in Russian).
    • (2003) Nonlinear Dynamics and Control , vol.3 , pp. 73-98
    • Magnitskii, N.A.1    Sidorov, S.V.2
  • 85
    • 3543101993 scopus 로고    scopus 로고
    • Finding homoclinic and heteroclinic contours of singular points of nonlinear systems of ordinary differential equations
    • Magnitskii, N.A. and Sidorov, S.V. (2003b). Finding homoclinic and heteroclinic contours of singular points of nonlinear systems of ordinary differential equations. Differential equations, 39, 11, pp. 1593-1602.
    • (2003) Differential equations , vol.39 , Issue.11 , pp. 1593-1602
    • Magnitskii, N.A.1    Sidorov, S.V.2
  • 86
    • 38849124428 scopus 로고    scopus 로고
    • Actual problems of chaotic dynamics in dissipative systems of nonlinear ordinary differential equations
    • Magnitskii, N.A. and Sidorov, S.V. (2004a). Actual problems of chaotic dynamics in dissipative systems of nonlinear ordinary differential equations. Dynamics of non-homogeneous systems, 7, pp. 5-43.
    • (2004) Dynamics of non-homogeneous systems , vol.7 , pp. 5-43
    • Magnitskii, N.A.1    Sidorov, S.V.2
  • 88
    • 15444380187 scopus 로고    scopus 로고
    • Rotor type singular points of non-autonomous systems of differential equations and their role in generation of singular attractors of nonlinear autonomous systems
    • Magnitskii, N.A. and Sidorov, S.V. (2004c). Rotor type singular points of non-autonomous systems of differential equations and their role in generation of singular attractors of nonlinear autonomous systems. Differential Equations, 40, 11, pp. 1579-1593.
    • (2004) Differential Equations , vol.40 , Issue.11 , pp. 1579-1593
    • Magnitskii, N.A.1    Sidorov, S.V.2
  • 89
    • 15244343469 scopus 로고    scopus 로고
    • Transition to chaos in the Lorenz system via a compete double homoclinic bifurcation cascade
    • Magnitskii, N.A. and Sidorov, S.V. (2005a). Transition to chaos in the Lorenz system via a compete double homoclinic bifurcation cascade. Computational Mathematics and Modelling, 16, 1, pp. 26-37.
    • (2005) Computational Mathematics and Modelling , vol.16 , Issue.1 , pp. 26-37
    • Magnitskii, N.A.1    Sidorov, S.V.2
  • 91
    • 30344458208 scopus 로고    scopus 로고
    • On transition to diffusion chaos through a subharmonic cascade of bifurcations of two-dimensional tori
    • Magnitskii, N.A. and Sidorov, S.V. (2005c). On transition to diffusion chaos through a subharmonic cascade of bifurcations of two-dimensional tori. Differential Equations, 41, 11, pp. 1550-1558.
    • (2005) Differential Equations , vol.41 , Issue.11 , pp. 1550-1558
    • Magnitskii, N.A.1    Sidorov, S.V.2
  • 95
    • 45949127771 scopus 로고
    • Different ways to turbulence in dissipative dynamical systems
    • Manneville, P. and Pomeau, Y. (1980). Different ways to turbulence in dissipative dynamical systems. Physica, 1D, p. 219.
    • (1980) Physica , vol.1D , pp. 219
    • Manneville, P.1    Pomeau, Y.2
  • 97
    • 0003588811 scopus 로고    scopus 로고
    • Stable and random motions in dynamical systems
    • Princeton Univ. Press
    • Moser, J. (2001). Stable and random motions in dynamical systems. UK Nonlinear News, 25. Princeton Univ. Press, 210p.
    • (2001) UK Nonlinear News , vol.25 , pp. 210
    • Moser, J.1
  • 102
    • 85079420785 scopus 로고    scopus 로고
    • On one nonlinear model with complex dynamics
    • in Russian
    • Novikov, M.D. and Pavlov, B.M. (2000). On one nonlinear model with complex dynamics. Vestnik MSU, 2, pp. 3-7 (in Russian).
    • (2000) Vestnik MSU , vol.2 , pp. 3-7
    • Novikov, M.D.1    Pavlov, B.M.2
  • 106
    • 0000186307 scopus 로고    scopus 로고
    • Estimating model parameters from times series by autosyn-chronization
    • Parlitz, U. (1996). Estimating model parameters from times series by autosyn-chronization. Phys. Rev. Lett, 76, pp. 1232-1235.
    • (1996) Phys. Rev. Lett , vol.76 , pp. 1232-1235
    • Parlitz, U.1
  • 111
    • 34250315551 scopus 로고
    • Continuous control of chaos by self-controlling feedback
    • Pyragas, K. (1992). Continuous control of chaos by self-controlling feedback. Phys. Lett. A., 170, pp. 421-428.
    • (1992) Phys. Lett. A. , vol.170 , pp. 421-428
    • Pyragas, K.1
  • 112
    • 0007603733 scopus 로고
    • Stochastic self-modulation of waves in non equilibrium environments
    • Rabinovich, M.I. and Fabrikant, A.L. (1979). Stochastic self-modulation of waves in non equilibrium environments. Zh. Eksp. Teor. Fiz., 77, pp. 617-629.
    • (1979) Zh. Eksp. Teor. Fiz. , vol.77 , pp. 617-629
    • Rabinovich, M.I.1    Fabrikant, A.L.2
  • 113
    • 0004043484 scopus 로고
    • Second edition. CRC Press, New York
    • Robinson, C. (1995). Dynamical systems. Second edition. CRC Press, New York.
    • (1995) Dynamical systems
    • Robinson, C.1
  • 114
    • 49549126801 scopus 로고
    • An equation for continuous chaos
    • Rossler, O.E. (1976). An equation for continuous chaos. Phys. Lett. A, 57, 5, pp. 397-398.
    • (1976) Phys. Lett. A , vol.57 , Issue.5 , pp. 397-398
    • Rossler, O.E.1
  • 115
    • 34250451946 scopus 로고
    • On the nature of turbulence
    • Ruelle, D. and Takens, F. (1971). On the nature of turbulence. Commun. Math. Phys., 20, 3, pp. 167-192.
    • (1971) Commun. Math. Phys. , vol.20 , Issue.3 , pp. 167-192
    • Ruelle, D.1    Takens, F.2
  • 116
    • 33744833457 scopus 로고
    • Generalized synchronization of chaos in directional coupled chaotic systems
    • Rulkov, N.F., Sushchik, M.M., Tsimring, L.S. and Abarbanel, H.D. (1995). Generalized synchronization of chaos in directional coupled chaotic systems. Phys. Rev. E, 51, 2, pp. 980-994.
    • (1995) Phys. Rev. E , vol.51 , Issue.2 , pp. 980-994
    • Rulkov, N.F.1    Sushchik, M.M.2    Tsimring, L.S.3    Abarbanel, H.D.4
  • 117
    • 0000670926 scopus 로고
    • Finite amplitude free convection as an initial value problem
    • Saltzman, B. (1981). Finite amplitude free convection as an initial value problem. J. Atraos. Sci, 19, p. 329.
    • (1981) J. Atraos. Sci , vol.19 , pp. 329
    • Saltzman, B.1
  • 120
    • 0000203285 scopus 로고
    • Controlling chaos in a network of oscillators
    • Sepulchre, J. and Babloyantz, A. (1994). Controlling chaos in a network of oscillators. Phys. Rev., E48, 2, pp. 119-125.
    • (1994) Phys. Rev. , vol.E48 , Issue.2 , pp. 119-125
    • Sepulchre, J.1    Babloyantz, A.2
  • 122
    • 0002072428 scopus 로고
    • Cycles coexistence of continuous transformation of line in itself
    • Sharkovskii, A.N. (1964). Cycles coexistence of continuous transformation of line in itself. Ukr. Math. Journal, 26, 1, pp. 61-71.
    • (1964) Ukr. Math. Journal , vol.26 , Issue.1 , pp. 61-71
    • Sharkovskii, A.N.1
  • 124
    • 0002995706 scopus 로고
    • A contribution to the problem of the structure of an extended neighborhood of a rough equilibrium state of saddle-focus type
    • Shilʼnikov, L.P. (1970). A contribution to the problem of the structure of an extended neighborhood of a rough equilibrium state of saddle-focus type. Math. USSR Sb., 81(123), 1, pp. 92-103.
    • (1970) Math. USSR Sb. , vol.81 , Issue.123
    • Shilʼnikov, L.P.1
  • 126
    • 4244116032 scopus 로고
    • Chua’s circuit: Rigorous results and future problems
    • Shilʼnikov, L.P. (1994). Chua’s circuit: rigorous results and future problems. Int. J. Bifurcation and Chaos, 4, 3, pp. 488-519.
    • (1994) Int. J. Bifurcation and Chaos , vol.4 , Issue.3 , pp. 488-519
    • Shilʼnikov, L.P.1
  • 128
    • 0000601493 scopus 로고
    • Using small perturbations to control chaos
    • 1993
    • Shinbort, T., Grebogi, C. and Yorke, J.A. (1993). Using small perturbations to control chaos. Nature, 363, 3, 1993, pp. 411-417.
    • (1993) Nature , vol.363 , Issue.3 , pp. 411-417
    • Shinbort, T.1    Grebogi, C.2    Yorke, J.A.3
  • 129
    • 84927896522 scopus 로고
    • Dynamical systems with elastic mappings. Ergodic properties of scattering billiards
    • in Russian
    • Sinai, J.G. (1970). Dynamical systems with elastic mappings. Ergodic properties of scattering billiards. Russ. Math. Surv., 25, 2, pp. 141-192 (in Russian).
    • (1970) Russ. Math. Surv. , vol.25 , Issue.2 , pp. 141-192
    • Sinai, J.G.1
  • 131
    • 0001014007 scopus 로고
    • Structurally stable systems are not dense
    • Smale, S. (1966). Structurally stable systems are not dense. Amer. J. Math., 88, pp. 491-496.
    • (1966) Amer. J. Math. , vol.88 , pp. 491-496
    • Smale, S.1
  • 132
    • 84968514104 scopus 로고
    • Differentiable dynamical systems
    • Smale, S. (1967). Differentiable dynamical systems. Bull. Amer. Math. Soc, 73, pp. 747-817.
    • (1967) Bull. Amer. Math. Soc , vol.73 , pp. 747-817
    • Smale, S.1
  • 133
    • 0002587254 scopus 로고    scopus 로고
    • Mathematical problems for the next century
    • Smale, S. (1998). Mathematical problems for the next century. Math. Intelligencer, 20, 2, pp. 7-15.
    • (1998) Math. Intelligencer , vol.20 , Issue.2 , pp. 7-15
    • Smale, S.1
  • 139
    • 0002061016 scopus 로고    scopus 로고
    • A rigorous ODE solver and Smale’s 14th problem
    • Tucker, W. (2002). A rigorous ODE solver and Smale’s 14th problem. Found. Comput. Math., pp. 53-117.
    • (2002) Found. Comput. Math. , pp. 53-117
    • Tucker, W.1
  • 140
  • 141
    • 0002367246 scopus 로고
    • A chaotic dynamical system
    • Vallis, G.K. (1986). A chaotic dynamical system. Science, 232, pp. 243-245.
    • (1986) Science , vol.232 , pp. 243-245
    • Vallis, G.K.1
  • 142
    • 0007012141 scopus 로고
    • Conceptual models of El Nino
    • Vallis, G.K. (1988). Conceptual models of El Nino. J. Geophys. Res., 93, pp. 13979-13991.
    • (1988) J. Geophys. Res. , vol.93 , pp. 13979-13991
    • Vallis, G.K.1
  • 144
    • 51249180360 scopus 로고
    • The structure of the Lorenz attractors
    • Williams, R.F. (1979). The structure of the Lorenz attractors. Publ. Math. IHES, 50, pp. 321-347.
    • (1979) Publ. Math. IHES , vol.50 , pp. 321-347
    • Williams, R.F.1
  • 145
    • 0002573630 scopus 로고
    • Metastable chaos: The transition to sustained chaos oscillations in a model of Lorenz
    • Yorke, J.A. and Yorke, E.O. (1979). Metastable chaos: the transition to sustained chaos oscillations in a model of Lorenz. J. Stat. Phys., 21, pp. 263-277.
    • (1979) J. Stat. Phys. , vol.21 , pp. 263-277
    • Yorke, J.A.1    Yorke, E.O.2
  • 147
    • 85129077643 scopus 로고    scopus 로고
    • Classification of chaos in 3-d autonomous quadratic systems. I: Basic framework and methods
    • accepted
    • Zhou, T. and Chen, G. (2005). Classification of chaos in 3-d autonomous quadratic systems. I: Basic framework and methods. Int. J. of Bifur. Chaos, accepted.
    • (2005) Int. J. of Bifur. Chaos
    • Zhou, T.1    Chen, G.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.