HOMOCLINIC AND HETEROCLINIC MOTIONS IN HYBRID SYSTEMS WITH IMPACTS

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Fen M. O., Fen F. T.

MATHEMATICA SLOVACA, vol.67, no.5, pp.1179-1188, 2017 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 67 Issue: 5
  • Publication Date: 2017
  • Doi Number: 10.1515/ms-2017-0041
  • Journal Name: MATHEMATICA SLOVACA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1179-1188
  • Keywords: impulsive systems, stable and unstable sets, homoclinic motion, heteroclinic motion, Duffing equation with impacts, NEURAL-NETWORKS, IMPULSIVE ODE, CHAOS, STABILITY, SYNCHRONIZATION, COMMUNICATION
  • TED University Affiliated: Yes

Abstract

In this paper, we present a method to generate homoclinic and heteroclinic motions in impulsive systems. We rigorously prove the presence of such motions in the case that the systems are under the influence of a discrete map that possesses homoclinic and heteroclinic orbits. Simulations that support the theoretical results are represented by means of a Duffing equation with impacts. (C) 2017 Mathematical Institute Slovak Academy of Sciences