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In this paper an approach to generate hidden attractors based on piecewiselinear (PWL) systems is studied. The approach consists of the coexistence ofself-excited attrators and hidden attractors, i.e., the equilibria of thesystem are immersed in the basin of attraction of the seft-excited attractors,so hidden attractors appear around these self-excited attractors. The approachstarts by generating a double-scroll attractor based on two equilibriapresented heteroclinic orbits. Then, two equilibria are added to the system, sobiestability is generated by displaying two self-excited attractor. In thispaper we show that hidden attractors arise as a consequence of the rupture oftrajectories that resemble heteroclinic orbits at a larger scale. Therefore,multistability appears naturally as an interesting phenomenon present in thisclass of dynamical systems via hidden attractors and self-excited attractors.The study suggests the feasibility of the geometric design of new classes ofmultistable systems with coexistence of the two classes of attractors or evenmultistable systems without equilibria at all.

Coexistence of hidden attractors and self-excited attractors through breaking heteroclinic-like orbits of switched systems