Bifurcation of Periodic Orbits of a Three-Dimensional Piecewise Smooth System

Abstract

We consider a three-dimensional piecewise smooth system having an invariant surface and a closed orbit of multiplicity k on the invariant surface. By using bifurcation techniques and analyzing the number of solutions of bifurcation equations, we study certain bifurcation phenomena near the multiple k closed orbit and obtain some conditions for the existence of periodic orbits bifurcated from it. Moreover, our partial analytical results are demonstrated by some examples.