[PDF][PDF] Smale Horseshoes and Ši'lnikov Chaos in a New Three-Order Dynamical System
2017•arastirmax.com
This paper presents the existence of Ši'lnikov homoclinic and heteroclinic orbits in the novel
system by using the undetermined coefficient method. The Ši'lnikov criterion along with
some technical conditions guarantees that the novel system has both Smale horseshoes
and the horseshoe chaos. Moreover, it is shown that the heteroclinic and homoclinic orbits
together determine the geometric structure of attractors.
system by using the undetermined coefficient method. The Ši'lnikov criterion along with
some technical conditions guarantees that the novel system has both Smale horseshoes
and the horseshoe chaos. Moreover, it is shown that the heteroclinic and homoclinic orbits
together determine the geometric structure of attractors.
Abstract
This paper presents the existence of Ši'lnikov homoclinic and heteroclinic orbits in the novel system by using the undetermined coefficient method. The Ši'lnikov criterion along with some technical conditions guarantees that the novel system has both Smale horseshoes and the horseshoe chaos. Moreover, it is shown that the heteroclinic and homoclinic orbits together determine the geometric structure of attractors.
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