Memristor Synapse-Driven Simplified Hopfield Neural Network: Hidden Dynamics, Attractor Control, and Circuit Implementation

Detection of hidden dynamics is of great value in model prediction and control engineering. To explore its effects and control methods in the memristive network model, this paper presents a memristor synapse-driven ReLU-type Hopfield neural network (MRHNN). The generalized Hamilton function is derived from Helmholtz's theorem and the equilibrium points of the model are analyzed. It is found via numerical computations that because of no existence of equilibrium, the MRHNN model always unfolds hidden dynamics, including hidden bifurcation, hidden mode transition, hidden transient chaos, and hidden multistability. In addition, amplitude and offset boosting control of hidden attractors are executed, illustrating the flexibility of the attractor regulation. Finally, based on digital hardware devices, circuit experiments are deployed and their measurements well agree with the numerical results, certifying the dynamical effects and lossless control of the memristive neural network and physical reliability of the electronic neuron.