Dynamics of a Bistable Current-Controlled Locally-Active Memristor

Abstract

This paper presents a novel current-controlled locally-active memristor model to reveal the switching and oscillating characteristics of locally-active devices. It is shown that the memristor has two asymptotically stable equilibrium points on its power-off plot and therefore exhibits nonvolatility. Switching from one stable equilibrium point to another is achieved by applying a suitable current pulse. The locally-active characteristic of the memristor is measured by the DC [Formula: see text]–[Formula: see text] plot. A small-signal equivalent circuit on a locally-active operating point with the bias current [Formula: see text] is constructed for describing the characteristic of the locally-active region of the memristor. A periodic oscillator circuit composed of the locally-active memristor, a compensation inductor and a resistor is proposed, whose dynamics is analyzed in detail by using the Hopf bifurcation and the zeros and poles of the impendence function of the circuit. It is found that the locally-active memristor based circuit with different current biases or different initial conditions can exhibit different dynamics such as periodic oscillation and stable equilibrium point. If an energy storage element (capacitor) is added to the periodic oscillation circuit, a chaotic oscillator is obtained, which can exhibit abundant dynamics. The oscillation mechanism of the memristor-based oscillator is analyzed via dynamic route map (DRM), showing that the memristor is an essential device for generating periodic and chaotic oscillations, and its local activity is the cause for complex oscillations.