메뉴 건너뛰기




Volumn 12, Issue 1, 2011, Pages 106-118

Dynamical analysis of a new autonomous 3-D chaotic system only with stable equilibria

Author keywords

Chaotic attractors; Degenerate heteroclinic cycles; Lyapunov exponent; Poincar map; Sil'nikov theorem

Indexed keywords

CHAOTIC ATTRACTORS; HETEROCLINIC CYCLES; LYAPUNOV EXPONENT; POINCAR MAP; SIL'NIKOV THEOREM;

EID: 77957997353     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2010.05.038     Document Type: Article
Times cited : (122)

References (29)
  • 1
    • 0000241853 scopus 로고
    • Deterministic non-periodic flow
    • E.N. Lorenz Deterministic non-periodic flow J. Atmospheric Sci. 20 1963 130 141
    • (1963) J. Atmospheric Sci. , vol.20 , pp. 130-141
    • Lorenz, E.N.1
  • 2
    • 49549126801 scopus 로고
    • An equation for continuous chaos
    • O.E. Rssler An equation for continuous chaos Phys. Lett. A 57 1976 397 398
    • (1976) Phys. Lett. A , vol.57 , pp. 397-398
    • Rssler, O.E.1
  • 3
    • 33751555569 scopus 로고
    • Some simple chaotic flows
    • J.C. Sprott Some simple chaotic flows Phys. Rev. E 50 1994 647 650
    • (1994) Phys. Rev. e , vol.50 , pp. 647-650
    • Sprott, J.C.1
  • 4
    • 0034645889 scopus 로고    scopus 로고
    • A new class of chaotic circuit
    • J.C. Sprott A new class of chaotic circuit Phys. Lett. A 266 2000 19 23
    • (2000) Phys. Lett. A , vol.266 , pp. 19-23
    • Sprott, J.C.1
  • 5
    • 0041322255 scopus 로고    scopus 로고
    • Simplest dissipative chaotic flow
    • J.C. Sprott Simplest dissipative chaotic flow Phys. Lett. A 228 1997 271 274
    • (1997) Phys. Lett. A , vol.228 , pp. 271-274
    • Sprott, J.C.1
  • 7
  • 8
    • 39449106074 scopus 로고    scopus 로고
    • Chaotic attractors of the conjugate Lorenz-type system
    • Q.G. Yang, G.R. Chen, and K.F. Huang Chaotic attractors of the conjugate Lorenz-type system Internat. J. Bifur. Chaos 17 2007 3929 3949
    • (2007) Internat. J. Bifur. Chaos , vol.17 , pp. 3929-3949
    • Yang, Q.G.1    Chen, G.R.2    Huang, K.F.3
  • 9
    • 0347740484 scopus 로고    scopus 로고
    • The diffusionless Lorenz equations: Sil'nikov bifurcations and reduction to an explicit map
    • G. van der Schrier, and L.R.M. Maas The diffusionless Lorenz equations: Sil'nikov bifurcations and reduction to an explicit map Physica D 141 2000 19 36
    • (2000) Physica D , vol.141 , pp. 19-36
    • Van Der Schrier, G.1    Maas, L.R.M.2
  • 10
    • 0009520409 scopus 로고
    • Strange attractor, chaotic behaviour and information flow
    • R. Shaw Strange attractor, chaotic behaviour and information flow Z. Naturforsch. 36A 1981 80 112
    • (1981) Z. Naturforsch. , vol.36 , pp. 80-112
    • Shaw, R.1
  • 11
    • 47749084301 scopus 로고    scopus 로고
    • A chaotic system with one saddle and two stable node-foci
    • Q.G. Yang, and G.R. Chen A chaotic system with one saddle and two stable node-foci Internat. J. Bifur. Chaos 18 2008 1393 1414
    • (2008) Internat. J. Bifur. Chaos , vol.18 , pp. 1393-1414
    • Yang, Q.G.1    Chen, G.R.2
  • 12
    • 77955512357 scopus 로고    scopus 로고
    • Nonlinear analysis in a Lorenz-like system
    • 10.1016/j.nonrwa.2009.12.010
    • F.S. Dias, L.F. Mello, and J.G. Zhang Nonlinear analysis in a Lorenz-like system Nonlinear Anal. RWA 2009 10.1016/j.nonrwa.2009.12.010
    • (2009) Nonlinear Anal. RWA
    • Dias, F.S.1    Mello, L.F.2    Zhang, J.G.3
  • 14
    • 0242425114 scopus 로고    scopus 로고
    • Complex dynamical behaviors of the chaotic Chen's system
    • T.S. Zhou, G.R. Chen, and Y. Tang Complex dynamical behaviors of the chaotic Chen's system Internat. J. Bifur. Chaos 13 2003 2561 2574
    • (2003) Internat. J. Bifur. Chaos , vol.13 , pp. 2561-2574
    • Zhou, T.S.1    Chen, G.R.2    Tang, Y.3
  • 15
    • 33845517878 scopus 로고    scopus 로고
    • A unified Lorenz-type system and its canonical form
    • Q.G. Yang, G.R. Chen, and T.S. Zhou A unified Lorenz-type system and its canonical form Internat. J. Bifur. Chaos 16 2006 2855 2871
    • (2006) Internat. J. Bifur. Chaos , vol.16 , pp. 2855-2871
    • Yang, Q.G.1    Chen, G.R.2    Zhou, T.S.3
  • 16
    • 48249085183 scopus 로고    scopus 로고
    • Existence of a singularly degenerate heterclinic cycle in the Lorenz system and its dynamical consequences: Part 1*
    • H. Kokubu, and R. Roussarie Existence of a singularly degenerate heterclinic cycle in the Lorenz system and its dynamical consequences: part 1* J. Dyn. Differ. Equ. 16 2004 513 557
    • (2004) J. Dyn. Differ. Equ. , vol.16 , pp. 513-557
    • Kokubu, H.1    Roussarie, R.2
  • 17
    • 67650921905 scopus 로고    scopus 로고
    • Dynamics at infinity and the existence of singularly degenerate heteroclinic cycles in the Lorenz system
    • M. Messias Dynamics at infinity and the existence of singularly degenerate heteroclinic cycles in the Lorenz system J. Phys. A: Math. Theor. 42 2009 115101
    • (2009) J. Phys. A: Math. Theor. , vol.42 , pp. 115101
    • Messias, M.1
  • 18
    • 60949105862 scopus 로고    scopus 로고
    • Degenerate Hopf bifurcations in the L system
    • L.F. Mello, and S.F. Coelho Degenerate Hopf bifurcations in the L system Phys. Lett. A 373 2009 1116 1120
    • (2009) Phys. Lett. A , vol.373 , pp. 1116-1120
    • Mello, L.F.1    Coelho, S.F.2
  • 19
    • 40849136288 scopus 로고    scopus 로고
    • Bifurcation analysis of a new Lorenz-like chaotic system
    • L.F. Mello, M. Messias, and D.C. Braga Bifurcation analysis of a new Lorenz-like chaotic system Chaos Solitons Fractals 37 2008 1244 1255
    • (2008) Chaos Solitons Fractals , vol.37 , pp. 1244-1255
    • Mello, L.F.1    Messias, M.2    Braga, D.C.3
  • 20
    • 0027648847 scopus 로고
    • New treatment on bifurcation of periodic solutions and homoclinic orbits at high r in the Lorenz equations
    • J. Li, and J. Zhang New treatment on bifurcation of periodic solutions and homoclinic orbits at high r in the Lorenz equations SIAM J. Appl. Math. 53 1993 1059 1071
    • (1993) SIAM J. Appl. Math. , vol.53 , pp. 1059-1071
    • Li, J.1    Zhang, J.2
  • 21
    • 1642303941 scopus 로고    scopus 로고
    • Hopf bifurcation analysis in the L system
    • Y. Yu, and S. Zhang Hopf bifurcation analysis in the L system Chaos Solitons Fractals 21 2004 1215 1220
    • (2004) Chaos Solitons Fractals , vol.21 , pp. 1215-1220
    • Yu, Y.1    Zhang, S.2
  • 22
    • 18544393481 scopus 로고    scopus 로고
    • Periodic orbits and bomoclinic orbits of the diffusionless Lorenz equations
    • D. Huang Periodic orbits and bomoclinic orbits of the diffusionless Lorenz equations Phys. Lett. A 309 2003 248 253
    • (2003) Phys. Lett. A , vol.309 , pp. 248-253
    • Huang, D.1
  • 23
    • 70349989954 scopus 로고    scopus 로고
    • Controlling the diffusionless Lorenz equations with periodic parametric perturbation
    • Z.C. Wei, and Q.G. Yang Controlling the diffusionless Lorenz equations with periodic parametric perturbation Comput. Math. Appl. 58 2009 1979 1987
    • (2009) Comput. Math. Appl. , vol.58 , pp. 1979-1987
    • Wei, Z.C.1    Yang, Q.G.2
  • 24
    • 0001234956 scopus 로고
    • A case of the existence of a countable number of periodic motions
    • L.P. Sil'nikov A case of the existence of a countable number of periodic motions Sov. Math. Docklady 6 1965 163 166
    • (1965) Sov. Math. Docklady , vol.6 , pp. 163-166
    • Sil'Nikov, L.P.1
  • 25
    • 84956230541 scopus 로고
    • A contribution of the problem of the structure of an extended neighborhood of rough equilibrium state of saddlefocus type
    • L.P. Sil'nikov A contribution of the problem of the structure of an extended neighborhood of rough equilibrium state of saddlefocus type Math. USSR-Shornik 10 1970 91 102
    • (1970) Math. USSR-Shornik , vol.10 , pp. 91-102
    • Sil'Nikov, L.P.1
  • 27
    • 0033240334 scopus 로고    scopus 로고
    • The Rikitake two-disk dynamo system and domains with periodic orbits
    • Y. Hardy, and W.H. Steeb The Rikitake two-disk dynamo system and domains with periodic orbits Int. J. Theor. Phys. 38 1999 2413 2417
    • (1999) Int. J. Theor. Phys. , vol.38 , pp. 2413-2417
    • Hardy, Y.1    Steeb, W.H.2
  • 28
    • 58149492531 scopus 로고    scopus 로고
    • Global dynamics of Rikitake system
    • J. Llibre, and M. Messias Global dynamics of Rikitake system Physica D 238 2009 241 252
    • (2009) Physica D , vol.238 , pp. 241-252
    • Llibre, J.1    Messias, M.2
  • 29
    • 0034721624 scopus 로고    scopus 로고
    • Invariant algebraic surfaces of the Rikitake system
    • J. Llibre, and X. Zhang Invariant algebraic surfaces of the Rikitake system J. Phys. A: Math. Gen. 33 2000 7613 7635
    • (2000) J. Phys. A: Math. Gen. , vol.33 , pp. 7613-7635
    • Llibre, J.1    Zhang, X.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.