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

doi:10.1007/s10483-013-1736-7

Applied Mathematics and Mechanics (English Edition) ›› 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”

A. ALGABA¹ F.FERN´ANDEZ-S´ANCHEZ² M. MERINO¹ A.J.RODR´IGUEZ-LUIS²

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:2012-11-27 Revised:2013-04-01 Online:2013-09-02 Published:2013-09-02

Abstract

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

2010 MSC Number:

65P20

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”. Applied Mathematics and Mechanics (English Edition), 2013, 34(9): 1175-1176.

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URL: https://www.amm.shu.edu.cn/EN/10.1007/s10483-013-1736-7

https://www.amm.shu.edu.cn/EN/Y2013/V34/I9/1175

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