On the limit cycles of a class of piecewise linear differential systems in R-4 with two zones

Abstract

We study the bifurcation of limit cycles from the periodic orbits of a four-dimensional center in a class of piecewise linear differential systems with two zones. Our main result shows that three is an upper bound for the number of limit cycles that bifurcate from a center, up to first order expansion of the displacement function. Moreover, this upper bound is reached. The main technique used is the averaging method. (C) 2011 IMACS. Published by Elsevier B.V. All rights reserved.