Generating Grid Multi-Scroll Attractors in Memristive Neural Networks

Memristors are well suited as artificial nerve synapses owing to its unique memory function. This paper establishes a novel flux-controlled memristor model using hyperbolic function series. By taking the memristor as synapses in a Hopfield neural network (HNN), three memristive HNNs are constructed. These memristive HNNs can generate multi-double-scroll chaotic attractors or grid multi-double-scroll chaotic attractors. The number of double scrolls in the attractors is controlled by the memristor. Equilibrium points analysis further reveals the generation mechanism of grid multi-double-scroll chaotic attractors. Moreover, numerical simulations indicate the existence of complex dynamics in the memristive HNNs, including extreme multistability and amplitude control. An approach to physically realize grid multi-double-scroll chaotic attractors is also given. Finally, an encryption scheme based on the proposed memristive HNN is designed to demonstrate application potential of the attractors.