Dual memristive Hopfield neural networks: Bistable coexistence attractor and image encryption

This paper proposes a novel dual memristive Hopfield neural network (HNN) system which can generate coexisting attractors. The time-domain waveform and hysteresis loop of two memristors are displayed. And the dynamic behavior is shown with different dual memristors' parameters. Particularly, based on the characteristic that the equilibrium point of the system is symmetrical about the origin, we select two initial values which are symmetrical about the origin such as 0.1,0.1,0.1 and -0.1,-0.1,-0.1, find a pair of bistable coexisting attractors, and analyze their dynamic behavior such as coexisting bifurcation diagrams and Lyapunov exponents (LEs). And we design a new encryption process. It provides new ideas for research on memristor-coupled HNN.