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Perturbed Li-Yorke homoclinic chaos

Akhmet, Marat
Feckan, Michal
Fen, Mehmet Onur
Kashkynbayev, Ardak
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.