Non-Autonomous ReLU-Type Hopfield Neural Network Model

Neural networks play a crucial role in neuromorphic computing and intelligent systems. For the Hopfield neural networks (HNN), despite much research focus on autonomous models, practical scenarios often involve external influences with time-varying stimuli, which requires exploration of the dynamical effects on the non-autonomous HNN model. This study investigates a simple ReLU-type HNN model with alternating current (AC) inputs first. Then, the ones influenced by the amplitude parameter are revealed. Numerical results confirm that complex phenomena occur including chaos, quasi-period, transient states, and coexisting attractors. Finally, an electrical circuit is used to verify the influence of a time-varying external environment on such a neural network, and the measured results on the analog level are consistent with the numerical simulations. Certainly, such the neural network will disclose the behaviors of large-scale network clusters and the engineering applications of artificial intelligence.