On Hopf bifurcation of Liu chaotic system

Abstract In this paper, we analyze the dynamical behaviors of Liu system using the complementary-cluster energy-barrier criterion (CCEBC). Moreover, the Hopf bifurcation of this system is investigated using the first Lyapunov coefficient. Also, it is proved that this system has two Hopf bifurcation points, at which these Hopf bifurcations are non degenerate and subcritical.

[1]  Guanrong Chen,et al.  Bifurcation Analysis of Chen's equation , 2000, Int. J. Bifurc. Chaos.

[2]  Yongguang Yu,et al.  Hopf bifurcation in the Lü system , 2003 .

[3]  Samuel Bowong,et al.  A New Adaptive Chaos Synchronization Principle for a Class of Chaotic Systems , 2005 .

[4]  Guanrong Chen,et al.  From Chaos To Order Methodologies, Perspectives and Applications , 1998 .

[5]  M. T. Yassen,et al.  Adaptive chaos control and synchronization for uncertain new chaotic dynamical system , 2006 .

[6]  Guanrong Chen,et al.  Analysis of a new chaotic system , 2005 .

[7]  Guanrong Chen,et al.  On the generalized Lorenz canonical form , 2005 .

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

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

[10]  Guanrong Chen,et al.  The compound structure of a new chaotic attractor , 2002 .

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

[12]  Guanrong Chen,et al.  Dynamical Analysis of a New Chaotic Attractor , 2002, Int. J. Bifurc. Chaos.

[13]  J. A. Kuznecov.  Elements of applied bifurcation theory , 1998 .

[14]  Zhenya Yan.  Hopf bifurcation in the Lorenz-type chaotic system , 2007 .

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

[16]  Xiaobing Zhou,et al.  Hopf bifurcation analysis of the Liu system , 2008 .

[17]  Guanrong Chen,et al.  On a four-dimensional chaotic system , 2005 .

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

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

[20]  Tao Liu,et al.  A Modified Lorenz System , 2006 .