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Applied Mathematics and Mechanics (English Edition) ›› 2013, Vol. 34 ›› Issue (9): 1175-1176.doi: https://doi.org/10.1007/s10483-013-1736-7

• 论文 • 上一篇    

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. 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
  • 收稿日期:2012-11-27 修回日期:2013-04-01 出版日期:2013-09-02 发布日期:2013-09-02

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. 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

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摘要： 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.

关键词: homoclinic chaos, heteroclinic chaos, non-existence of Shilnikov chaos

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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