Phase-locking in weakly heterogeneous neuronal networks

TL;DR

This paper analytically investigates how weak heterogeneity affects the existence and stability of phase-locked states in neuronal networks with all-to-all coupling, revealing conditions for stable synchronization and effects of increasing heterogeneity.

Contribution

It provides a theoretical framework for understanding phase-locking stability in heterogeneous neuronal networks, extending previous homogeneous models.

Findings

Stable phase-locking persists under weak heterogeneity if homogeneous states are stable.

Increasing heterogeneity can destabilize or eliminate phase-locked states.

The analysis characterizes network states when phase-locking breaks down.

Abstract

We examine analytically the existence and stability of phase-locked states in a weakly heterogeneous neuronal network. We consider a model of N neurons with all-to-all synaptic coupling where the heterogeneity is in the firing frequency or intrinsic drive of the neurons. We consider both inhibitory and excitatory coupling. We derive the conditions under which stable phase-locking is possible. In homogeneous networks, many different periodic phase-locked states are possible. Their stability depends on the dynamics of the neuron and the coupling. For weak heterogeneity, the phase-locked states are perturbed from the homogeneous states and can remain stable if their homogeneous conterparts are stable. For enough heterogeneity, phase-locked solutions either lose stability or are destroyed completely. We analyze the possible states the network can take when phase-locking is broken.