Perturbed Li–Yorke homoclinic chaos

Abstract

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 outside the scrambled sets is demonstrated. Control methods such as Ott–Grebogi–Yorke and Pyragas are utilized to stabilize these quasi‑periodic motions. A Duffing oscillator model illustrates the theoretical findings with supporting simulations.