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

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.