A novel locally active time-delay memristive Hopfield neural network and its application

Hopfield neural network is an import cornerstone of neural network research. The dynamic analysis has always been a hot topic of the Hopfield neural network research. Memristor, the fourth-generation electronic device, is considered to be ideal nonlinear device applied in neural networks. In this work, we propose a novel time-delay locally active memristor, which has abundant dynamical behaviors. Characteristics of the proposed memristor are analyzed by power-off plot, DC V–I plot and pinched hysteresis loops plot. We applied the novel time-delay locally active memristor to a Hopfield neural to investigate the dynamic of the network. It is interesting that the proposed neural network has abundant dynamic behaviors, such as coexisting attractors, chaotic attractors and hyperchaotic attractors. The interesting phenomena are illustrated through bifurcation diagram, Lyapunov exponents diagram, and phase portraits. The electrical circuit of the proposed memristor and the Hopfield neural network is designed and simulated. The circuit simulation results are well consistent with the numerical simulation. Moreover, we propose an application of the Hopfield neural network to chaotic image encryption. Histogram, correlation, information entropy, and key sensitivity show that the simple image encryption scheme has high security and reliable encryption performance.