Analyzing Stability of Equilibrium Points in Neural Networks: A General Approach

TL;DR

This paper introduces a general method to determine explicit constraints on coupling strengths in neural networks to ensure the stability of equilibrium points, demonstrated through models of coupled excitatory-inhibitory oscillators.

Contribution

A novel, general methodology for deriving explicit stability constraints in coupled neural systems, applicable to various models.

Findings

Derived explicit stability constraints for neural network equilibria.

Validated approach on excitatory-inhibitory oscillator models.

Provided a framework for stability analysis under parameter variations.

Abstract

Networks of coupled neural systems represent an important class of models in computational neuroscience. In some applications it is required that equilibrium points in these networks remain stable under parameter variations. Here we present a general methodology to yield explicit constraints on the coupling strengths to ensure the stability of the equilibrium point. Two models of coupled excitatory-inhibitory oscillators are used to illustrate the approach.