Heteroclinic cycles in a class of 3-dimensional piecewise affine systems

It is well known that homoclinic and heteroclinic cycles can potentially result in chaos in dynamical systems. However, it is not easy to find the homoclinic or heteroclinic cycles in concrete systems. Therefore, how to prove the existence of homoclinic and heteroclinic cycles is an important problem in modern dynamical systems. In this paper, for a class of 3-dimensional piecewise affine systems we present succinct sufficient conditions for the existence of three types of heteroclinic cycles by mathematical analysis. As applications, two existence results of chaotic invariant sets are obtained. In addition, some examples are presented to illustrate our results.