A new memristor-based fractional-order chaotic system

Abstract

In this paper, a new four-dimensional incommensurate fractional-order system is proposed by introducing an ideal flux-controlled memristor into a three-dimensional chaotic system, and combining it with fractional-order calculus theory, which is solved by using the Adomian decomposition method (ADM). Through theoretical analysis we found the system has numerous equilibrium points. Compared with the original system, the modified system exhibits richer dynamical behaviors. The main manifestations are: (i) Antimonotonicity varying with the initial value. (ii) Three kinds of transient transition behaviors: transient asymptotically-period (A-period), transient chaos, and tri-state transition (chaos-A-period-chaos). (iii) Initial offset boosting behavior. (iv) Hidden extreme multistability. (v) As the order q changes, the system is capable of generating a variety of asymptotically periodic attractors and chaotic attractors. These behaviors above are analyzed in detail by means of numerical simulations such as phase diagram, bifurcation diagram, Lyapunov exponent spectrum (LEs), time-series diagram, and attraction basin. Finally, the system is implemented with a hardware circuit based on a digital signal processor (DSP), which in turn proved the correctness of the numerical analysis simulations and the physical realizability of the system.