Multi-stable hidden attractor chaotic system and its analog coexistence circuit realization

Abstract

Abstract This paper proposes a multi-stable chaotic system with relatively complex hidden attractors. The dynamic performance of chaotic systems is under investigation via numerical simulations such as Lyapunov exponents, division diagrams, and phase diagrams, and it has been further found that the chaotic system with hidden attractors can switch between the two cases of having no equilibrium or having two stable equilibria. Due to the system’s symmetry, multiple co-existing attractors can be obtained by choosing appropriate parameters and initial values. It is demonstrated that the system exhibits a multi-stability phenomenon, which means that different initial conditions generate two or more different dynamics. In addition, the variational method is used to explore short-period orbits of a topological length up to 3, which provides a deeper understanding of the essential components of a chaotic system. Finally, circuit implementation verifies its correctness and feasibility.