Sliding Homoclinic Bifurcations in a Class of Three-Dimensional Piecewise Affine Systems

This paper studies sliding homoclinic bifurcations in a class of symmetric three-zone three-dimensional piecewise affine systems. The systems have one parameter and the unperturbed systems have a pair of sliding homoclinic orbits to a saddle. Based on the analysis of the one-dimensional Poincaré maps, two types of sliding cycles are obtained from the sliding homoclinic bifurcations of the systems. In addition, two examples of sliding homoclinic orbits and sliding cycles are provided with simulations to illustrate the effectiveness of the theorems.