Heteroclinic Cycles Generated by Piecewise Affine Systems in ℝⁿ

It is essential yet challenging to investigate heteroclinic trajectories in chaotic dynamics of high-dimensional systems. This paper presents an efficient approach for precise prediction of heteroclinic cycles in n-dimensional (n ≥ 3) piecewise affine systems. Moreover, it systemically investigates different types of heteroclinic cycles in the considered systems, and proposes the corresponding existence conditions with rigorous proofs by analyzing the dynamics of stable and unstable manifolds. In addition, three numerical examples with both a heteroclinic cycle and a chaotic set are provided to verify the established results.