Far East Journal of Dynamical Systems
Volume 19, Issue 1, Pages 25 - 38
(May 2012)
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SI’LNIKOV HOMOCLINIC ORBITS IN A 4D ASYMMETRIC SYSTEM
Weiqin Yu and Fangqi Chen
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Abstract:
In the present paper, a 4D asymmetric system is considered. By applying the undetermined coefficient method, Si’lnikov homoclinic orbits in this system are found analytically and the uniform convergence of the corresponding series expansions of the homoclinic orbits is proved. As a consequence, the Si’lnikov criterion guarantees that the system has Smale horseshoe chaos and the geometric structures of attractors are determined. |
| Keywords and phrases: homoclinic orbit, attractor, Si’lnikov criterion, chaos. |
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