Dynamical mechanism of a memristor and its phase transition

Abstract A device is defined as a memristor if it exhibits a pinched hysteresis loop in the current–voltage plane, and the loop area shrinks with increasing driven frequency until it gets a single-valued curve. However, the explaination of the underlying mechanism for these fingerprints is still limited. In this paper, we propose the differential form of the memristor function, and we disclose the dynamical mechanism of the memristor according to the differential form. The symmetry of the curve is only determined by the driven signal, and the shrinking loop area results from the shrinking area enclosed by driven signal and the time coordinate axis. Significantly, we find the condition for the phase transition of a memristor, and the resistance switches between the positive resistance, local zero resistance, and local negative resistance. This phase transition is confirmed in the HP memristor. These results advance the understanding of the dynamics mechanism and phase transition of a memristor.