Bifurcation of periodic orbits and its application for high-dimensional piecewise smooth near integrable systems with two switching manifolds

Abstract

In this paper, we study the bifurcation of periodic orbits for high-dimensional piecewise smooth near integrable systems defined in three regions separated by two switching manifolds. We assume that the unperturbed system has a family of periodic orbits which cross two switching manifolds transversely. The expression of Melnikov function is derived based on the first integral. And the conditions of periodic orbits bifurcated from a family of periodic orbits for the high-dimensional piecewise smooth near integrable system are obtained. The theoretical results are applied to the bifurcation analysis of periodic orbits of two-degree-of-freedom piecewise smooth system of nonlinear energy sink. The periodic orbits configurations are presented with numerical method and the number of periodic orbits is three.