Hopf Bifurcation and Chaos in Simplest Fractional-Order Memristor-based Electrical CircuitReport as inadecuate




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1 JAD - Laboratoire Jean Alexandre Dieudonné

Abstract : In this article, we investigate the bifurcation and chaos in a simplest fractional-ordermemristor-based electrical circuit composed of only three circuit elements: a linear passive capacitor,a linear passive inductor and a non-linear active memristor with two-degree polynomial memristanceand a second-order exponent internal state. It is shown that this fractional circuit can exhibita drastically rich non-linear dynamics such as a Hopf bifurcation, coexistence of two, three and fourlimit cycles, double-scroll chaotic attractor, four-scroll chaotic attractor, coexistence of one or twochaotic attractor with one limit cycle and new chaotic attractor which is not observed in the integercase. Finally, the presence of chaos is confirmed by the application of the recently introduced 0–1test.

Keywords : Fractional derivative Memristor Chaos Electrical circuit Hopf bifurcation Dynamical system Strange attractor





Author: Mohammed-Salah Abdelouahab - René Lozi -

Source: https://hal.archives-ouvertes.fr/



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