Dynamics Analysis of Fractional-Order Memristive Time-Delay Chaotic System and Circuit Implementation

The integer-order memristive time-delay chaotic system has attracted much attention and has been well discussed. However, the fractional-order system is closer to the real system. In this paper, a nonlinear time-delay chaotic circuit based on fractional-order memristive system was proposed. Some dynamical properties, including equilibrium points, stability, bifurcation, and Lyapunov exponent of the oscillator, were investigated in detail by theoretical analyses and simulations. Moreover, the nonlinear phenomena of coexisting bifurcation and attractor was found. The phenomenon shows that the state of this oscilator was highly sensitive to its initial value, which is called coexistent oscillation in this paper. Finally, the results of the system circuit simulation accomplished by Multisim were perfectly consistent with theoretical analyses and numerical simulation.