RESUMEN

Stable stationary solutions correspond to memory capacity in the application of associative memory for neural networks. In this presentation, existence of multiple stable stationary solutions for Hopfield-type neural networks with delay and without delay is investigated. Basins of attraction for these stationary solutions are also estimated. Such a scenario of dynamics is established through formulating parameter conditions based on a geometrical setting. The present theory is demonstrated by two numerical simulations on the Hopfield neural networks with delays.

RESUMEN

We use singular perturbation theory to analyze the dynamics of N weakly interacting pulses in a one-dimensional synaptically coupled neuronal network. The network is modeled in terms of a nonlocal integro-differential equation, in which the integral kernel represents the spatial distribution of synaptic weights, and the output activity of a neuron is taken to be a mean firing rate. We derive a set of N coupled ordinary differential equations (ODEs) for the dynamics of individual pulses, establishing a direct relationship between the explicit form of the pulse interactions and the structure of the long-range synaptic coupling. The system of ODEs is used to explore the existence and stability of stationary N-pulses and traveling wave trains.