Persistence of Li–Yorke chaos in systems with relay

Autor: Marat Akhmet, Mehmet Onur Fen, Ardak Kashkynbayev
Jazyk: angličtina
Rok vydání: 2017
Předmět:
Zdroj: Electronic Journal of Qualitative Theory of Differential Equations, Vol 2017, Iss 72, Pp 1-18 (2017)
Druh dokumentu: article
ISSN: 1417-3875
DOI: 10.14232/ejqtde.2017.1.72
Popis: 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.
Databáze: Directory of Open Access Journals