Coexistence of singular cycles in a class of three-dimensional piecewise affine systems

Singular cycles (homoclinic orbits and heteroclinic cycles) play an important role in the study of chaotic dynamics of dynamical systems. This paper provides the coexistence of singular cycles that intersect the switching manifold transversely at two points in a class of three-dimensional two-zone piecewise affine systems. Moreover, the switching manifold of the systems is constructed by two perpendicular planes. Different to the three-dimensional piecewise affine systems with a switching plane, the system can ensure the coexistence of two homoclinic orbits to the same one equilibrium point and two heteroclinic cycles constructing by three heteroclinic orbits. In addition, three examples with simulations of the singular cycles are provided to illustrate the effectiveness of the results.