Bifurcation analysis and chaos in simplest fractional-order electrical circuit

Abstract

In this paper we investigate the bifurcation and chaos in a fractional-order simplest electrical circuit composed of only three circuit element: a linear passive capacitor, a linear passive inductor and a nonlinear active memristor with two degree polynomial memristance and a second order exponent internal state. It is shown that this fractional circuit can exhibit rich nonlinear dynamics such as a Hopf bifurcation, double scroll chaotic attractor, four scroll chaotic attractor and new chaotic attractor which is not observed in the integer case. Finally, the presence of chaos is confirmed by the application of the recently introduced 0-1 test.