Dynamics of a fractional order locally-active Memristor with applications in oscillatory systems*

Abstract A non-volatile fractional-order Memristor, with two asymptotically stable equilibrium points and locally-active characteristic is presented. A fractional-order small-signal equivalent circuit is used to describe the memristor’s characteristics at an operating point within a locally-active region. Via the equivalent circuit, the memristor is shown to possess an edge of chaos within a voltage range; when connected in series with an inductor, it generates periodic oscillation about the locally-active operating point in the edge of chaos. The oscillating frequency and the external inductance are determined by the small-signal circuit’s admittance. Adding external capacitors and inductors in series/parallel with the memristor, three- and four-dimensional circuits are realized which generates chaotic oscillations. Analysis of the resulting three- and four-dimensional circuits are carried out at the memristor’s equilibrium point, the effects of the memristor’s parameters and the fractional order indexes of the added components on the system dynamics are also investigated using Lyapunov and bifurcation analysis. Numerical simulations show the versatility of the memristor for usages in oscillatory systems.