Adaptation controls synchrony and cluster states of coupled threshold-model neurons

TL;DR

This paper extends the master stability approach to analyze synchrony and cluster states in delay-coupled threshold-model neurons, revealing how adaptation and coupling types influence network stability and synchronization.

Contribution

It introduces a generalized method for studying stability in non-smooth dynamical systems with adaptive neurons, including heterogeneous populations and activity-based adaptation effects.

Findings

Subthreshold adaptation affects synchrony stability depending on excitation or inhibition dominance.

Synchrony is unstable in balanced recurrent synaptic input networks.

Synchronization properties are similar across different network topologies under certain conditions.

Abstract

We analyze zero-lag and cluster synchrony of delay-coupled non-smooth dynamical systems by extending the master stability approach, and apply this to networks of adaptive threshold-model neurons. For a homogeneous population of excitatory and inhibitory neurons we find (i) that subthreshold adaptation stabilizes or destabilizes synchrony depending on whether the recurrent synaptic excitatory or inhibitory couplings dominate, and (ii) that synchrony is always unstable for networks with balanced recurrent synaptic inputs. If couplings are not too strong, synchronization properties are similar for very different coupling topologies, i.e., random connections or spatial networks with localized connectivity. We generalize our approach for two subpopulations of neurons with non-identical local dynamics, including bursting, for which activity-based adaptation controls the stability of cluster states, independent of a specific coupling topology.