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 (i omega,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 Y-P (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. (C) 2021 Elsevier Ltd. All rights reserved.