Multistable Behaviors Analysis and Sliding Mode Control of Fractional-order Memristive Hindmarsh–Rose Neuron

In this paper, based on the existing 3D memristor Hindmarsh–Rose (HR) neuron model, a fractional-order model is constructed and numerically solved by Adomian decomposition method. The influence of fractional-order q on the system is analyzed by using bifurcation diagram, Spectral entropy(SE)/C0 complexity, 0-1 test and other algorithms, it is found that the multistable characteristics of the system are more complex under fractional-order behavior. The effects of coupling parameters of external stimulus current and memristor on the multistability of the system are also studied. Then, based on the sliding mode control theory, chaos synchronization controller of the system are designed, Matlab simulation results show that the controller is realizable and effective, and also has the characteristics of fast response, which provides a reference for the control and application of memristor neural network system.