Nonlinear analysis in a Lorenz-like system

Abstract In this paper we study the nonlinear dynamics of a Lorenz-like system. More precisely, we study the stability and bifurcations which occur in a new three parameter quadratic chaotic system. We also study the existence of singularly degenerate heteroclinic cycles for a suitable choice of the parameters. As a consequence we show the existence of chaotic attractors when these cycles disappear.

[1]  Chongxin Liu,et al.  A new chaotic attractor , 2004 .

[2]  Luis Fernando Mello,et al.  Degenerate Hopf bifurcations in the Lü system , 2009 .

[3]  T. Rikitake,et al.  Oscillations of a system of disk dynamos , 1958, Mathematical Proceedings of the Cambridge Philosophical Society.

[4]  Y. Chu,et al.  Chaos and chaos synchronization for a non-autonomous rotational machine systems , 2008 .

[5]  C. Sparrow.  The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors , 1982 .

[6]  O. Rössler.  An equation for continuous chaos , 1976 .

[7]  L. S. Pontryagin,et al.  Ordinary Differential Equations , 1963 .

[8]  Marcelo Messias,et al.  Dynamics at infinity and the existence of singularly degenerate heteroclinic cycles in the Lorenz system , 2009 .

[9]  A. Wolf,et al.  Determining Lyapunov exponents from a time series , 1985 .

[10]  E. Lorenz.  Deterministic nonperiodic flow , 1963 .

[11]  Jinhu Lu,et al.  A New Chaotic Attractor Coined , 2002, Int. J. Bifurc. Chaos.

[12]  Marcelo Messias,et al.  Bifurcation analysis of a new Lorenz-like chaotic system , 2008 .

[13]  Y. Ilyashenko,et al.  Finiteness Theorems for Limit Cycles , 1991 .

[14]  Denis de Carvalho Braga,et al.  Hopf Bifurcations in a Watt Governor with a Spring , 2008, 0802.4438.

[15]  Qigui Yang,et al.  A Chaotic System with One saddle and Two Stable Node-Foci , 2008, Int. J. Bifurc. Chaos.

[16]  Leon O. Chua,et al.  Chua's Circuit: an Overview Ten Years Later , 1994, J. Circuits Syst. Comput..

[17]  Y. Kuznetsov.  Elements of Applied Bifurcation Theory , 2023, Applied Mathematical Sciences.

[18]  W. D. Evans,et al.  PARTIAL DIFFERENTIAL EQUATIONS , 1941 .

[19]  Jiangang Zhang,et al.  Nonlinear dynamics and circuit implementation for a new Lorenz-like attractor , 2009 .

[20]  Hiroshi Kokubu,et al.  Existence of a Singularly Degenerate Heteroclinic Cycle in the Lorenz System and Its Dynamical Consequences: Part I , 2004 .

[21]  Denis de Carvalho Braga,et al.  Bifurcation analysis of the Watt governor system , 2006 .

[22]  Zhidong Teng,et al.  Analysis of an SIR Epidemic Model with Pulse Vaccination and Distributed Time Delay , 2007, Journal of biomedicine & biotechnology.

[23]  Alberto Tesi,et al.  Harmonic balance methods for the analysis of chaotic dynamics in nonlinear systems , 1992, Autom..

[24]  Guanrong Chen,et al.  YET ANOTHER CHAOTIC ATTRACTOR , 1999 .

[25]  Lansun Chen,et al.  A delayed epidemic model with stage-structure and pulses for pest management strategy , 2008 .