A Discrete Memristive Hopfield Neural Network With Grid Multi-structure/scroll-like Attractors

In constructing memristive neural networks, memristors’ intrinsic memory and synapse plasticity characteristics endow the neural networks with complex nonlinear dynamics. However, discrete memristive neural networks with grid multi-structure/scroll-like attractors have not been reported. In this work, a novel discrete memristive Hopfield neural network (DMHNN) is presented by coupling a discrete memristor simulating the mutual synapse into a Hopfield neural network. Multi-structure/scroll-like hyperchaotic attractors are revealed under the control of coupling strength. Interestingly, by adjusting the network parameters, the system can generate diverse grid-structure/scroll-like attractors with different arrangements, which is a chaotic behavior that previous discrete neural networks do not possess. For different sets of network parameters, DMHNN can exhibit multidirectional initial offset-boosting phenomena and can control an arbitrary number of coexisting homogeneous attractors. FPGA-based hardware circuit is designed, and grid multi-structure/scroll-like attractors are successfully implemented. Furthermore, DMHNN is applied to a pseudo-random number generator (PRNG) to evaluate its randomness performance.