Dynamical analysis and circuit implementation of ReLU-type Hopfield neural network under bipolar pulse stimuli

Abstract Complex electrophysiological environments have profound impacts on neuronal electrical activities. To explore the regulatory effects of time-varying current including amplitude, angular frequency, and bias on neural networks, this paper proposes a ReLU-type Hopfield neural network (RHNN) model under bipolar pulse stimuli. Theoretical analysis reveals the existence of the hyperbolic equilibrium points, which exhibit unstable states with the change of the stimuli. Besides, the Hamilton energy function of the presented RHNN model is calculated, which is related to the membrane potentials of two neurons. Numerical simulations further uncover a wide range of dynamical behaviors induced by variations in the driving parameters, including periodic, limit cycle, and chaotic states. Additionally, the paper identifies coexisting attractor phenomena triggered by changes in initial conditions of neurons, such as the coexistence of different periodic orbits, periodic and chaotic states, as well as periodic and quasi-periodic trajectories. An electronic circuit without multipliers is designed, and the experimental results on the analog level align well with the numerical analyses. In addition, the image encryption application utilizing the complexity of the chaotic sequences of the RHNN model is successfully implemented. These findings demonstrate that the forcing bipolar pulse stimuli can significantly induce complex dynamics in neural networks, providing theoretical foundations and technical support for future research on neural dynamic systems and intelligent hardware circuit design.