Adomian Decomposition, Firing Change Process Analysis and Synchronous Control of Fractional-Order Hindmarsh–Rose Neurons in Electromagnetic Field

In this paper, based on integer-order Hindmarsh–Rose (HR) neurons under an electric field, the fractional-order model is constructed, and the nonlinear term is decomposed by the Adomian decomposition method, and the numerical solution of the system is obtained. The firing behavior of the neuron model is analyzed by using a phase diagram, interspike interval (ISI) bifurcation diagram, sample entropy (SE) complexity, and largest Lyapunov exponent (LLE). Based on the sliding mode control theory, a chaos synchronization controller of the system is designed. Matlab simulation results show that the controller is realizable and effective, and also has the characteristic of fast response, which provides a reference for the control and application of a memristor neural network system.