Perturbed Li-Yorke homoclinic chaos

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10.14232ejqtde.2018.1.75.pdf

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2018-01-01

Author

Akhmet, Marat
Fen, Mehmet Onur
Kashkynbayev, Ardak

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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.

Subject Keywords

Applied Mathematics, Homoclinic orbit, Li-Yorke chaos, Almost periodic orbits, Duffing oscillator

URI

https://hdl.handle.net/11511/39832

Journal

ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS

DOI

https://doi.org/10.14232/ejqtde.2018.1.75

Collections

Department of Mathematics, Article

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Citation Formats

M. Akhmet, M. O. Fen, and A. Kashkynbayev, “Perturbed Li-Yorke homoclinic chaos,” ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, pp. 1–18, 2018, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/39832.