A bistable nonvolatile locally-active memristor and its complex dynamics

This paper introduces a novel bistable nonvolatile locally-active memristor model based on Chua's unfolding theorem to explore the influence of the local activity on the complexity of nonlinear systems. It is shown that the memristor has two asymptotically stable equilibrium points in its power-off plot with a negative memductance and a positive memductance, namely, it is nonvolatile. It is then shown that the fast switching between the two stable equilibrium points can be implemented by applying an appropriate voltage pulse. It is found that the memristor possesses four locally-active regions in its DC V-I plot, and a small signal equivalent circuit associated with a locally-active operating point of the memristor is designed using the small-signal analysis method, to explore its locally-active characteristics. Based on the small signal equivalent circuit, it is furthermore demonstrated that the nonvolatile locally-active memristor, when connected in parallel with a linear capacitor, oscillates periodically around a locally-active operating point via Hopf bifurcation. The dynamics of the memristor and its periodic oscillation are analyzed using the theory of local activity, pole-zero analysis of admittance functions, Hopf bifurcation and the edge of chaos. Finally, it is found that a chaotic oscillation evolved from the periodic oscillation appears by adding an energy-storage element (inductor) on the periodic oscillating circuit, which leads to the chaotic oscillation, coexisting attractors and various complex dynamical phenomena.