Persistence of Li-Yorke chaos in systems with relay

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

ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, vol.2017, no.72, pp.1-18, 2017 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 2017 Issue: 72
  • Publication Date: 2017
  • Doi Number: 10.14232/ejqtde.2017.1.72
  • 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: persistence of chaos, Li-Yorke chaos, almost periodic motions, relay system, chaos control, GENERALIZED SYNCHRONIZATION, DYNAMICAL-SYSTEMS, PERTURBATIONS, ENTRAINMENT, OSCILLATOR, FEEDBACK, SPACES
  • TED University Affiliated: Yes

Abstract

It is rigorously proved that the chaotic dynamics of the non-smooth system with relay function is persistent even if a chaotic perturbation is applied. We consider chaos in a modified Li-Yorke sense such that there are infinitely many almost periodic motions embedded in the chaotic attractor. It is demonstrated that the system under investigation possesses countable infinity of chaotic sets of solutions. An example that supports the theoretical results is represented. Moreover, a chaos control procedure based on the Ott-Grebogi-Yorke algorithm is proposed to stabilize the unstable almost periodic motions.