Dynamic Analysis of Fractional-Order Memristive Chaotic System

Abstract

For the purpose of investigating the nonlinear dynamics of the system, a fractional-order Chua's circuit based on the memristor deriving from the integer-order counterparts is provided.Firstly, according to the Lyapunov's indirect method, the stability analysis of the memristive system is made, and it shows that when the fractional-orders parameter of memristive system passes a critical value, the system loses the stability and bifurcation occurs.Then the bifurcation and chaos behaviors of fractional-order memristive system are shown using bifurcation diagrams with varying fractional orders of the system and other parameters.Furthermore, the chaotic behaviors of memristive chaotic system are proved by the waveform, phase plot and largest Lyapunov exponent diagram.Finally, theoretical results are illustrated and validated with the given numerical simulations.