Predicting the oscillation condition of memristor-based oscillators using Hopf bifurcation theory

摘要

This paper addresses mainly to the analysis of the emerging memristor-based oscillators. This novel oscillator, unable to be expressed in the form of the feedback system, cannot be analyzed using the conventional Barkhausen criterion. Here we propose an oscillation condition analysis method based on Hopf bifurcation theory, in which we introduce the first Lyapunov coefficient to determine whether the Hopf bifurcation is subcritical or supercritical. After having validated the proposed method by an ideal memristor based Van der Pol (VDP) oscillator as an example, we applied this method to the generic memristor based oscillator and predicted successfully its oscillation condition. The latter is not ideal model but a generic model derived from the real circuit. The simulation results of the propose method is very close to the direct simulation of the oscillator, but the propose method is 3 times faster.