Persistence of Li-Yorke chaos in systems with relay

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10.14232-ejqtde.2017.1.72.pdf

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2017-01-01

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Akhmet, Marat
Kashkynbayev, Ardak

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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.

Subject Keywords

Persistence of chaos, Li-Yorke chaos, Almost periodic motions, Relay system, Chaos control

URI

https://hdl.handle.net/11511/45882

Journal

ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS

DOI

https://doi.org/10.14232/ejqtde.2017.1.72

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Department of Mathematics, Article

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Citation Formats

M. Akhmet and A. Kashkynbayev, “Persistence of Li-Yorke chaos in systems with relay,” ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, pp. 1–18, 2017, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/45882.