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

作　　者：A.ALGABA F.FERNANDEZ-SANCHEZ M.MERINO A.J.RODRIGUEZ-LUIS 

机构地区：[1]Departamento de Matematicas,Centro de Investigacion de Fisica Teorica y Matematica FIMAT,University of Huelva [2]Departamento de Matematica Aplicada II,E.S.Ingenieros,University of Sevilla, Camino de los Descubrimientos s/n

出　　处：《Applied Mathematics and Mechanics(English Edition)》2013年第9期1175-1176,共2页应用数学和力学（英文版）

基　　金：supported by the Ministerio de Educacion y Ciencia,Plan Nacional I+D+I co-financed with FEDER Funds(No.MTM2010-20907-C02);the Consejeria de Educacion y Ciencia de la Juntade Andalucia(Nos.FQM-276,TIC-0130,and P08-FQM-03770)

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.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 

分 类 号：O322[理学—一般力学与力学基础]