Global Dynamics of Memristor Oscillator

Abstract

In this paper, we investigate the global dynamics of a memristor oscillator [Formula: see text] which comes from [Corinto et al., 2011], where [Formula: see text], and [Formula: see text]. Clearly, the case [Formula: see text] is trivial. So far, all results of this oscillator were given only for the case [Formula: see text], where the set of equilibria may change among a singleton, three points and a singular continuum and at most one limit cycle can arise and no limit cycles arise from the continuum. Compared with the case [Formula: see text], this oscillator displays more complicated dynamics for the case when [Formula: see text]. More clearly, one limit cycle may arise from the continuum and at most three limit cycles appear in the case of three equilibria, where generalized pitchfork bifurcation, saddle-node bifurcation, generalized Hopf bifurcation, double limit cycle bifurcation and homoclinic bifurcation may occur. Finally all global phase portraits are given for [Formula: see text] cases on the Poincaré disc, where a generalized normal sector method is applied. Moreover, our partial analytical results are demonstrated by numerical examples.