Collective activity bursting in networks of excitable systems adaptively coupled to a pool of resources

TL;DR

This paper investigates how feedback between a network of excitable units and a resource pool can induce collective bursting activity, using reduced mathematical models to explain the underlying mechanisms.

Contribution

It introduces a combined analytical approach using Ott-Antonsen reduction and singular perturbation theory to explain resource-driven bursting in adaptive networks.

Findings

Resource feedback induces bursting in the network.

Reduced models successfully capture the dynamics.

Oscillatory resource pools influence collective activity.

Abstract

We study the collective dynamics in a network of excitable units (neurons) adaptively interacting with a pool of resources. The resource pool is influenced by the average activity of the network, whereas the feedback from the resources to the network is comprised of components acting homogeneously or inhomogeneously on individual units of the network. Moreover, the resource pool dynamics is assumed to be slow and has an oscillatory degree of freedom. We show that the feedback loop between the network and the resources can give rise to collective activity bursting in the network. To explain the mechanisms behind this emergent phenomenon, we combine the Ott-Antonsen reduction for the collective dynamics of the network and singular perturbation theory to obtain a reduced system describing the interaction between the network mean field and the resources.