Stability of the dynamics of an asymmetric neural network

TL;DR

This paper analyzes the stability of large asymmetric neural networks with mixed excitatory and inhibitory interactions, providing conditions for divergence or stability of their dynamics.

Contribution

It introduces new sufficient conditions for the stability or divergence of large asymmetric neural networks with random Gaussian connectivity.

Findings

Identifies conditions leading to synchronized divergence.

Establishes criteria for stable neural network dynamics.

Analyzes large-scale network behavior.

Abstract

We study the stability of the dynamics of a network of n neurons intercting linearly through a random gaussian matrix of excitatory and inhibitory type. Using the aproach developed in a previous paper we show some interesting properties of the dynamic of this system for large values of n. We got sufficient conditions for getting diverging synchronized behavior or stability.