Coexisting singular cycles in a class of three-dimensional three-zone piecewise affine systems
This paper is concerned with the dynamics for a class of three-dimensional three-zone piecewise affine systems consisting of three sub-systems, one has a real eigenvalue and a pair of complex conjugate eigenvalues. The authors study the dynamics along the unstable and stable manifolds and prove that there exist three different types of coexisting singular cycles including homoclinic and homoclinic cycles, heteroclinic and heteroclinic cycles, homoclinic and heteroclinic cycles. Moreover, they obtain some sufficient conditions for chaotic invariant sets arising from these coexisting cycles.
scientific article; zbMATH DE number 7595644
scientific article