Dynamics Analysis and Hardware Implementation of Multi-Scroll Hyperchaotic Hidden Attractors Based on Locally Active Memristive Hopfield Neural Network

It is believed that local activation is the origin of all complexities, and the locally active memristive synaptic neural network can generate complex chaotic dynamic behaviors, such as hyperchaotic, multi-scroll, multi-stability and hidden dynamical behaviors. However, there are few studies on the simultaneous occurrence of multiple complex dynamic behaviors in neural networks. No chaotic system of multi-scroll hyperchaotic hidden attractors based on neural network has been found yet. To solve the problem, in this paper, we propose a new locally active memristive Hopfield neural network (HNN) model based on a multi-segment function, which is affected by electromagnetic radiation and external current. The multi-scroll hyperchaotic hidden attractors are found in the memristive HNN for the first time. Theoretical analysis and numerical simulation results show that the memristive HNN model has no equilibrium point, and the number of multi-scroll attractors is controlled by the state equation parameters of the memristive synapse. In addition, the structures and number of scrolls are also affected by electromagnetic radiation and external current. At the same time, under the appropriate parameter conditions, by modifying the initial value of the system, the memristive HNN has a controllable number of coexisting attractors, showing extreme multi-stability. Finally, a memristive HNN analog circuit is designed. The hardware experiment results reproduce the multi-scroll dynamics phenomenon, which verifies the correctness of the theoretical analysis and numerical simulation.