Characteristic Analysis of a Fractional-order Memristive Hyperchaotic System

Combining the ideal magnetic flux-controlled memristor with fractional-order calculus theory, a novel fractional-order memristor model was proposed. Through establishing the mathematical model of the fractional-order memristor, it was verified that the fractional-order memristor satisfies the fundamental characteristics of a memristor, and its memory performance is superior to that of integer-order memristors. Furthermore, the fractional-order memristor was introduced into a four-dimensional chaotic system, resulting in a new fractional-order memristor hyper-chaotic system, which was solved using the Adomian decomposition method. By studying the bifurcation diagrams and Lyapunov exponent spectra with the system’s order, parameters, and initial values as variables, it was observed that varying these factors leads to the manifestation of more complex and diverse dynamical behaviors in the system