Stability of Hopfield neural network with resistive and magnetic coupling

Abstract

Inspired by the interplay between both electrical and chemical synapses, we propose an analog electronic synapse-like model to characterize biological synaptic properties. By introducing the resistive and magnetic coupling, we consider hierarchical interconnection and the mixed couplings with two different kinds of coupling mechanisms. Meanwhile, based on Lyapunov function of the variable gradient method, stability of the Hopfield neural network with resistive and magnetic couplings was derived as the interconnection is symmetric and asymmetric, respectively. Furthermore, corresponding examples are calculated by using the numerical approach. The obtained results can be helpful to further develop brain-like systems based on the hierarchical Hopfield neural network with timing-dependent synaptic plasticity.