On homoclinic and heteroclinic orbits of Chen's System

We study the problem of existence of homoclinic and heteroclinic orbits of Chen's system. For the case of 2c > a > c > 0 and b ≥ 2a, we prove that the system has no homoclinic orbit but has two and only two heteroclinic orbits.

[1]  Lu Jun.  Chen's Chaotic Attractor and Its Characteristic Quantity , 2002 .

[2]  Guanrong Chen,et al.  On a Generalized Lorenz Canonical Form of Chaotic Systems , 2002, Int. J. Bifurc. Chaos.

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

[4]  M. T. Yassen,et al.  Chaos control of Chen chaotic dynamical system , 2003 .

[5]  Guanrong Chen,et al.  On stability and bifurcation of Chen’s system , 2004 .

[6]  Guanrong Chen,et al.  Chen's Attractor Exists , 2004, Int. J. Bifurc. Chaos.

[7]  J. Cowan.  Nonlinear oscillations, dynamical systems, and bifurcations of vector fields : John Guckenheimer and Philip Holmes Springer-Verlag, New York, 1983, 453 pp., $32.00 , 1986 .

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

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

[10]  Guanrong Chen,et al.  Local bifurcations of the Chen System , 2002, Int. J. Bifurc. Chaos.

[11]  P. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[12]  H. Agiza,et al.  Synchronization of Rossler and Chen chaotic dynamical systems using active control , 2001, Physics Letters A.

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

[14]  Daizhan Cheng,et al.  Bridge the Gap between the Lorenz System and the Chen System , 2002, Int. J. Bifurc. Chaos.

[15]  Xinghuo Yu,et al.  Detecting unstable periodic orbits in Chen's Chaotic Attractor , 2000, Int. J. Bifurc. Chaos.