Persistence of Li-Yorke chaos in systems with relay

Marat Akhmet, Mehmet Onur Fen, Ardak Kashkynbayev

Research output: Contribution to journalArticle

1 Citation (Scopus)

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.

Original languageEnglish
Article number72
JournalElectronic Journal of Qualitative Theory of Differential Equations
Volume2017
DOIs
Publication statusPublished - Jan 1 2017

Fingerprint

Li-Yorke Chaos
Periodic Motion
Almost Periodic
Chaos theory
Persistence
Relay
Chaos Control
Chaotic Attractor
Chaotic Dynamics
Countable
Chaos
Unstable
Infinity
Perturbation

Keywords

  • Almost periodic motions
  • Chaos control
  • Li-yorke chaos
  • Persistence of chaos
  • Relay system

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

Persistence of Li-Yorke chaos in systems with relay. / Akhmet, Marat; Fen, Mehmet Onur; Kashkynbayev, Ardak.

In: Electronic Journal of Qualitative Theory of Differential Equations, Vol. 2017, 72, 01.01.2017.

Research output: Contribution to journalArticle

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