Hidden dynamical behaviors, sliding mode control and circuit implementation of fractional-order memristive Hindmarsh−Rose neuron model

Abstract

In order to describe the complex dynamical behaviors of neurons with electromagnetic effect, this paper presents a fractional-order memristive (FOM) Hindmarsh–Rose (HR) neuron model by introducing a magnetic flux-controlled memristor to the three-dimensional HR neuron model. The proposed FOM HR neuron model without equilibrium point shows complex hidden dynamical behaviors, such as periodic orbits, chaotic behaviors, period-doubling bifurcations, and coexisting asymmetric phenomena, which are revealed by numerical simulations of local attraction basins, Lyapunov exponents, bifurcation diagrams, phase portraits, and so on. Furthermore, since most biomedical diseases are caused by abnormal discharge of neurons, a sliding mode control strategy is applied to suppress the chaotic behaviors of the FOM HR neuron model, which is helpful to prevent and treat diseases. Finally, we introduce the circuit designs of the FOM HR neuron model in detail, and the simulation results captured by oscilloscope in circuit implementation match well with the theoretical analysis.