Locally active memristor based oscillators: The dynamic route from period to chaos and hyperchaos

To explore the complexity of the locally active memristor and its application circuits, a tristable locally active memristor is proposed and applied in periodic, chaotic, and hyperchaotic circuits. The quantitative numerical analysis illustrated the steady-state switching mechanism of the memristor using the power-off plot and dynamic route map. For any pulse amplitude that can achieve a successful switching, there must be a minimum pulse width that enables the state variable to move beyond the attractive region of the equilibrium point. As local activity is the origin of complexity, the locally active memristor can oscillate periodically around a locally active operating point when connected in series with a linear inductor. A chaotic oscillation evolves from periodic oscillation by adding a capacitor in the periodic oscillation circuit, and a hyperchaotic oscillation occurs by further putting an extra inductor into the chaotic circuit. Finally, the dynamic behaviors and complexity mechanism are analyzed by utilizing coexisting attractors, dynamic route map, bifurcation diagram, Lyapunov exponent spectrum, and the basin of attraction.