Perturbed Li-Yorke homoclinic chaos

AKHMET M., Feckan M., Fen M. O., Kashkynbayev A.

ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, vol.2018, no.75, pp.1-18, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 2018 Issue: 75
  • Publication Date: 2018
  • Doi Number: 10.14232/ejqtde.2018.1.75
  • Journal Name: ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1-18
  • Keywords: homoclinic orbit, Li-Yorke chaos, almost periodic orbits, Duffing oscillator, DOUBLE SCROLL FAMILY, EQUATION, CIRCUIT, SYSTEM, RELAY
  • TED University Affiliated: Yes

Abstract

It is rigorously proved that a Li-Yorke chaotic perturbation of a system with a homoclinic orbit creates chaos along each periodic trajectory. The structure of the chaos is investigated, and the existence of infinitely many almost periodic orbits out of the scrambled sets is revealed. Ott-Grebogi-Yorke and Pyragas control methods are utilized to stabilize almost periodic motions. A Duffing oscillator is considered to show the effectiveness of our technique, and simulations that support the theoretical results are depicted.