Coexistence of singular cycles in a new kind of 3D non-smooth systems with two discontinuous boundaries

The aim here is to study complex dynamical behavior in a new kind of non-smooth systems with two discontinuous boundaries in space $$\mathbb {R}^3$$ . This paper provides an applicable method for accurately detecting coexistence of singular cycles, including (a) homoclinic and homoclinic cycles, (b) homoclinic and heteroclinic cycles, (c) heteroclinic and heteroclinic cycles. It is further proposed some criteria for guaranteeing three types of coexistence in the considered system. Moreover, existence conditions of chaos induced by such coexistence are established. Finally, three numerical examples are provided to verify the validity of theoretical results.

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