Initial boosting phenomenon of a fractional-order hyperchaotic system based on dual memristors

Abstract

In this paper, a fractional-order hyperchaotic system based on dual memristors is represented to analyze the nonlinear dynamic behaviors via replacing two coupled resistors with dual memristors. It is worthy to note that the fractional-order hyperchaotic system has two zero eigenvalues and three nonzero eigenvalues, therefore the equilibrium plane can be separated into diverse areas which indicates the hyperchaotic system is stable or chaotic. The simulation results illustrate that the initial states have a significant impact on the dynamic behaviors, which can be mirrored by the phase portraits, the bifurcation diagrams, the power spectrum and the time-domain waveform. In particular, the memristor initial boosting phenomenon is investigated in the proposed hyperchaotic system, which implies the memristor initial states determine the attractor offset boosting behaviors under various initial controllers. Clearly, it differs from the variable offset boosting behavior totally due to its multi-dimension and nonlinearity. Finally, numerical results under different initial controllers are exhibited to demonstrate the memristor initial boosting phenomenon. Moreover, a hardware circuit based on PSPICE software is fabricated and its experimental simulations is given to verify the dynamic behaviors effectively.