The complexity of dynamics in small neural circuits

TL;DR

This paper investigates the complex dynamics of small neural circuits, revealing how finite-size effects and symmetry-breaking lead to multiple solutions and richer behaviors beyond mean-field predictions.

Contribution

It introduces an analytically tractable framework for studying bifurcations and symmetry-breaking in small neural networks, highlighting phenomena absent in large-scale mean-field models.

Findings

Multiple branching solutions emerge through spontaneous symmetry-breaking.

Finite-size effects significantly influence neural dynamics.

Complex behaviors arise that are not captured by mean-field theory.

Abstract

Mean-field theory is a powerful tool for studying large neural networks. However, when the system is composed of a few neurons, macroscopic differences between the mean-field approximation and the real behavior of the network can arise. Here we introduce a study of the dynamics of a small firing-rate network with excitatory and inhibitory populations, in terms of local and global bifurcations of the neural activity. Our approach is analytically tractable in many respects, and sheds new light on the finite-size effects of the system. In particular, we focus on the formation of multiple branching solutions of the neural equations through spontaneous symmetry-breaking, since this phenomenon increases considerably the complexity of the dynamical behavior of the network. For these reasons, branching points may reveal important mechanisms through which neurons interact and process information, which are not accounted for by the mean-field approximation.