Bifurcation from Periodic Orbits of n-Dimensional Piecewise Smooth Differential Systems with Two Switching Planes

Abstract

In this paper, the general perturbation problem of piecewise smooth integrable differential systems with two switching planes is considered. Firstly, when the unperturbed system has a family of periodic orbits, we obtain the first order Melnikov vector function which can be used to study the number of periodic orbits bifurcated from the period annuli. Then, by using the obtained Melnikov vector function, we get an upper bound of the number of periodic orbits of a concrete [Formula: see text]-dimensional piecewise smooth differential system.