Initial State Dependent Nonsmooth Bifurcations in a Fractional-Order Memristive Circuit

Abstract

In this paper, Chua’s circuit model with a fractional-order memristor is proposed and investigated from the viewpoint of nonlinear dynamics. Unlike the previous fractional-order models as generalizations of integer-order memristive Chua’s circuit in the literature, by replacing all the first-order derivatives in the system equation with fractional-order derivatives, the proposed model has only one fractional-order derivative in the system equation, introduced on the basis of a physical observation. Stability and bifurcation are analyzed for a sub-system, and numerical simulation is done for the whole circuit system. “Intermittent chaos” resulting from tangent bifurcation or grazing bifurcation is found numerically, for which limit cycle and chaotic attractor switch with very high frequency. This is a typical feature of nonsmooth dynamic systems, and the nonsmoothness is caused mainly by the fractional-order derivative.