Chen's attractor exists

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Original languageEnglish
Pages (from-to)3167-3177
Journal / PublicationInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Issue number9
Publication statusPublished - Sep 2004


By applying the undetermined coefficient method, this paper finds homoclinic and heteroclinic orbits in the Chen system. It analytically demonstrates that the Chen system has one heteroclinic orbit of Ši'lnikov type that connects two nontrivial singular points. The Ši'lnikov criterion guarantees that the Chen system has Smale horseshoes and the horseshoe chaos. In addition, there also exists one homoclinic orbit joined to the origin. The uniform convergence of the series expansions of these two types of orbits are proved in this paper. It is shown that the heteroclinic and homoclinic orbits together determine the geometric structure of Chen's attractor.

Research Area(s)

  • Chen's attractor, Heteroclinic orbit, Homoclinic orbit, Ši'lnikov criterion