Stable Irregular Dynamics in Complex Neural Networks

TL;DR

This paper analytically investigates the microscopic irregular dynamics in finite neural networks, revealing that stable, non-chaotic irregular activity can arise and persist in inhibitory neural systems, contrasting with the common association of irregularity with chaos.

Contribution

The study provides a detailed analytical framework for understanding irregular neural activity in finite networks, showing stability of periodic orbits in inhibitory systems, which was previously less understood.

Findings

Irregular activity in inhibitory networks is stable and converges to periodic orbits.

Chaotic and stable dynamics can both produce irregular neural activity.

Finite network analysis reveals stability properties not captured by mean field theory.

Abstract

For infinitely large sparse networks of spiking neurons mean field theory shows that a balanced state of highly irregular activity arises under various conditions. Here we analytically investigate the microscopic irregular dynamics in finite networks of arbitrary connectivity, keeping track of all individual spike times. For delayed, purely inhibitory interactions we demonstrate that the irregular dynamics is not chaotic but rather stable and convergent towards periodic orbits. Moreover, every generic periodic orbit of these dynamical systems is stable. These results highlight that chaotic and stable dynamics are equally capable of generating irregular activity.