Comments on &ldquo;Non-existence of Shilnikov chaos in continuous-time systems&rdquo;

ZHAO Yong-xiang; YANG Bing; PENG Jia-chun; A. ALGABA; F.FERN′ANDEZ-S′ANCHEZ; M. MERINO; A.J.RODR′IGUEZ-LUIS

doi:10.1007/s10483-013-1736-7

Applied Mathematics and Mechanics >

2013 , Vol. 34 >Issue 9: 1175 - 1176

DOI: https://doi.org/10.1007/s10483-013-1736-7

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Comments on “Non-existence of Shilnikov chaos in continuous-time systems”

ZHAO Yong-xiang ,
YANG Bing ,
PENG Jia-chun ,
A. ALGABA ,
F.FERN′ANDEZ-S′ANCHEZ ,
M. MERINO ,
A.J.RODR′IGUEZ-LUIS

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1. Departamento de Matem´aticas, Centro de Investigaci´on de F´?sica Te´orica y Matem´atica FIMAT, University of Huelva, Huelva 21071, Spain;
2. Departamento de Matem´atica Aplicada II, E.S. Ingenieros, University of Sevilla, Camino de los Descubrimientos s/n, Sevilla 41092, Spain

Received date: 2012-11-27

Revised date: 2013-04-01

Online published: 2013-09-02

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Abstract

A paper, “Non-existence of Shilnikov chaos in continuous-time systems” was published in the journal Applied Mathematics and Mechanics (English Edition). The authors gave sufficient conditions for the non-existence of homoclinic and heteroclinic orbits in an nth-order autonomous system. Unfortunately, we show in this comment that the proof presented is erroneous and the result is invalid. We also provide two counterexamples of the wrong criterion stated by the authors.

Key words： fatigue; probabilistic S-N curves; reconstruction; Monte Carlo simulation; homoclinic chaos; heteroclinic chaos; non-existence of Shilnikov chaos

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ZHAO Yong-xiang , YANG Bing , PENG Jia-chun , A. ALGABA , F.FERN′ANDEZ-S′ANCHEZ , M. MERINO , A.J.RODR′IGUEZ-LUIS . Comments on “Non-existence of Shilnikov chaos in continuous-time systems”[J]. Applied Mathematics and Mechanics, 2013 , 34(9) : 1175 -1176 . DOI: 10.1007/s10483-013-1736-7

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