A memristive Hopfield neural network (HNN) model is proposed in which an improved multi-stable memristor is used to simulate coupled neuron synapses. Dynamical behavior of the model is analyzed and simulated with bifurcation diagram, Lyapunov exponential spectrum, phase plot and Poincare section. It shows that the memristive HNN generates chaotic attractors with different topologies and generates initial offset boosting highly dependent on initial value of the memristor. Finally, a chaotic image encryption scheme is designed based on the memristive HNN. The histogram, correlation, information entropy and key sensitivity are analyzed. It shows that the image encryption scheme resists effectively various internal and external statistical analysis attacks and has higher security.

A new memristor model is proposed and three memristive characteristics are analyzed with standard nonlinear theory.Analog circuit of the memristor is designed.Then, a memristor synapse-coupled ring Hopfield neural network is constructed based on the memristor synapse.Special dynamical behaviors closely related to the memristor synapse are revealed by adopting bifurcation diagrams, Lyapunov exponents, time series, etc.It shows that the memristive neural network generates multiple symmetrical bursting firing patterns and complex chaotic behavior at different memristive synaptic weight.Finally, an equivalent analog circuit of the memristive neural network is designed, and correctness of MATLAB numerical simulation is verified with PSIM circuit simulations.