Comment on ¡®?ilnikov-type orbits of Lorenz-family systems¡¯ [Physica A 375 (2007) 438-446]
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- 作者：Antonio Algaba ; Fern ; o Fern¨¢ndez-S¨¢nchez ; Manuel Merino ; Alej ; ro J. Rodr¨ªguez-Luis
- 关键词：Lorenz-family system ; Heteroclinic orbit ; &Scaron ; ilnikov criterion ; Undetermined coefficient method ; Chen system ; Lü ; system
- 刊名：Physica A
- 出版年：2013
- 出版时间：1 October, 2013
- 年：2013
- 卷：392
- 期：19
- 页码：4252-4257
- 全文大小：380 K
文摘
In the commented paper, the authors consider a four-parameter family of three-dimensional autonomous systems that includes the widely studied systems of Lorenz, Chen and L¨¹. Their goal is to rigorously prove the existence of ?ilnikov chaos in this Lorenz-family via the ?ilnikov criterion. They use an undetermined coefficient method to demonstrate the presence of heteroclinic orbits. In this comment we point out that their analysis is erroneous. The odd function they consider for the first component of the ?ilnikov heteroclinic orbit cannot represent such global connection. Thus, the main result of their paper, Theorem 2, is incorrect.