Heteroclinic cycles and chaos in a class of 3D three-zone piecewise affine systems

Abstract Little seems to be known about heteroclinic cycles and chaos in three-dimensional piecewise smooth dynamical systems with two or more discontinuous boundaries. This article presents a new class of three-dimensional three-zone piecewise affine systems with two discontinuous boundaries and provides some criteria for the existence of heteroclinic cycles in the following cases: (i) one saddle point and two focus points, (ii) two saddle points and one focus point, and (iii) three saddle points. Moreover, sufficient conditions for the existence of chaos are established. Finally, two numerical examples are provided to show the feasibility of our theoretical approach.