A tristable locally-active memristor and its complex dynamics

It has been well recognized that local activity is the origin of complex dynamics. Many important commercial applications would benefit from the locally-active memristors. To explore the locally active characteristics of memristors, a new tristable voltage-controlled locally-active memristor model is proposed based on Chua's unfolding theorem, which has three asymptotically equilibrium points and three locally-active regions. Non-volatility and the local activity of the memristor are demonstrated by POP (Power-Off Plot) and DC V-I plot. A small-signal equivalent circuit is established on a locally active operating point of the memristor to describe the characteristic of the memristor at the locally active region. Based on the admittance function Y(iω,V) of the small-signal equivalent circuit, the parasitic capacitor and the oscillation frequency of the are determined. The parasitic oscillation circuit consisting of the memristor, a parasitic resistor and a parasitic capacitor is analyzed in detail by Hopf bifurcation theory and the pole diagram of the composite admittance function YP (s, Q) of the parasitic oscillation circuit. Furthermore, by adding an inductor to the periodic parasitic circuit, we derive a simple chaotic circuit whose basic properties and coexisting dynamics are analyzed in detail. We concluded that the locally-active memristor provides the energy for the circuit to excite and maintain the periodic and chaotic oscillations.