Abstract:

Complexity and abundant dynamics may arise in locally-active systems only, in which locally-active elements are essential to amplify infinitesimal fluctuation signals and maintain oscillating. It has been recently found that some memristors may act as locally-active elements under suitable biasing. A number of important engineering applications would benefit from locally-active memristors. The aim of this paper is to show that locally-active memristor-based circuits can generate periodic and chaotic oscillations. To this end, we propose a non-volatile locally-active memristor, which has two asymptotically stable equilibrium points (or two non-volatile memristances) and globally-passive but locally-active characteristic. At an operating point in the locally-active region, a small-signal equivalent circuit is derived for describing the characteristics of the memristor near the operating point. By using the small-signal equivalent circuit, we show that the memristor possesses an edge of chaos in a voltage range, and that the memristor, when connected in series with an inductor, can oscillate about a locally-active operating point in the edge of chaos. And the oscillating frequency and the external inductance are determined by the small-signal admittance Y(iω). Furthermore, if the parasitic capacitor in parallel with the memristor is considered in the periodic oscillating circuit, the circuit generates chaotic oscillations.

Key words: memristor, chaos local activity, Hopf bifurcation