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Comment on “Sil’nikov chaos of the Liu system” [Chaos18, 013113 (2008)]
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1. L. Zhou and F. Chen, Chaos 18, 013113 (2008).
http://dx.doi.org/10.1063/1.2839909
http://aip.metastore.ingenta.com/content/aip/journal/chaos/21/4/10.1063/1.3657921
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/content/aip/journal/chaos/21/4/10.1063/1.3657921
2011-11-03
2015-05-25

Abstract

In the referenced paper, the authors use the undetermined coefficient method to prove analytically the existence of homoclinic and heteroclinic orbits in a Lorenz-like system. If the proof was correct, the existence of horseshoe chaos would be guaranteed via the Sil’nikov criterion. However, we hereby show that their demonstration is incorrect for two reasons. On the one hand, they wrongly use a symmetry the Lorenz-like system exhibits. On the other hand, they try to find structurally unstable global bifurcations by means of a series that is uniformly convergent in an open set of the parameter space: this would imply that the dynamical object they have found is structurally stable.

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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Comment on “Sil’nikov chaos of the Liu system” [Chaos18, 013113 (2008)]
http://aip.metastore.ingenta.com/content/aip/journal/chaos/21/4/10.1063/1.3657921
10.1063/1.3657921
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