Dynamic Analysis and Control of Fractional Order Memristor Hopfield Neural Network

In this paper, a novel smooth magnetron is introduced to construct a fractional memristor Hopfield neural network (fractional order M-HNN). The local stability of equilibrium point are analyzed theoretically. Taking the memristor coupling strength coefficient and the fractional order as bifurcation parameters, the phase trajectory diagram, the bifurcation diagram of the system are drawn to analyze the influence on the dynamic behavior of the neural network. When the system parameters are fixed, the hyperchaos phenomenon of the fractional order M-HNN model is revealed. Finally, the PD controller is applied to the model to enhance the stability of the system.