Extreme Multistability with Hidden Attractors in a Simplest Memristor-Based Circuit

A simplest memristor-based circuit as a quasi-Hamiltonian system with extreme multistability is proposed and analyzed. There is no equilibrium in the system, but chaotic, quasi-periodic and periodic hidden attractors are present. The coexisting bifurcation diagrams associated with the coexisting singular attractors are observed by varying the system parameters. Of particular interest is that the coexistence of an infinite number of hidden attractors for a set of system parameters is discovered. Finally, two routes to chaos, intermittent chaotic and transient chaotic routes, are analyzed systematically, which reveal the mechanisms of chaos generation in the new circuit system.