Homoclinical structure of the chaotic attractor

AKHMET M.

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, vol.15, no.4, pp.819-822, 2010 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 15 Issue: 4
  • Publication Date: 2010
  • Doi Number: 10.1016/j.cnsns.2009.05.042
  • Journal Name: COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.819-822
  • Keywords: Relay differential equations, Hyperbolic sets, Homoclinic solutions, Heteroclinic solutions
  • Middle East Technical University Affiliated: Yes

Abstract

In the reference [Akhmet MU. Devaney chaos of a relay system. Commun Nonlinear Sci Numer Simulat 2009:14:1486-93.], a relay system was introduced, which admits a chaotic attractor with Devaney's ingredients. Now, we prove that the attractor consists of homo-clinic solutions. A simulation of the attractor is provided for a pendulum equation. Similar results for impulsive differential equations were announced in the plenary talk [Akhmet MU. Hyperbolic sets of impact systems. Dyn Contin Discrete Impuls Syst Set A Math Anal 2008:15(Suppl. S1):1-2. Proceedings of the 5th international conference on impulsive and hybrid dynamical systems and applications, Beijin: Watan Press: 2008.]. (C) 2009 Elsevier B.V. All rights reserved.