Chaotic threshold of a class of hybrid piecewise-smooth system by an impulsive effect via Melnikov-type function

Abstract

<p style='text-indent:20px;'>In this paper, we study the chaotic behavior of a class of hybrid piecewise-smooth system incorporated into an impulsive effect (HPSS-IE) under a periodic perturbation. More precisely, we assume that the unperturbed system with a homoclinic orbit, it transversally jumps across the first switching manifold by an impulsive stimulation and continuously crosses the second switching manifold. Then the corresponding Melnikov-type function is derived. Based on the new Melnikov-type function, the bifurcation and chaotic threshold of the perturbed HPSS-IE are analyzed. Furthermore, numerical simulations are precisely demonstrated through a concrete example. The results indicate that it is an extension work of previous references.</p>