Inhibition causes ceaseless dynamics in networks of excitable nodes

TL;DR

Introducing inhibitory nodes into excitable networks can paradoxically lead to persistent, self-sustaining activity and avalanche dynamics, despite their activity-reducing effect, revealing a complex role of inhibition.

Contribution

This paper demonstrates that inhibition can induce ceaseless activity and critical avalanche behavior in excitable networks, a counterintuitive finding supported by theoretical analysis and simulations.

Findings

Inhibitory nodes can cause self-sustaining network activity.

Networks exhibit avalanche dynamics with universal scaling.

Inhibition plays a complex, non-intuitive role in network dynamics.

Abstract

The collective dynamics of a network of excitable nodes changes dramatically when inhibitory nodes are introduced. We consider inhibitory nodes which may be activated just like excitatory nodes but, upon activating, decrease the probability of activation of network neighbors. We show that, although the direct effect of inhibitory nodes is to decrease activity, the collective dynamics becomes self-sustaining. We explain this counterintuitive result by defining and analyzing a "branching function" which may be thought of as an activity-dependent branching ratio. The shape of the branching function implies that for a range of global coupling parameters dynamics are self-sustaining. Within the self-sustaining region of parameter space lies a critical line along which dynamics take the form of avalanches with universal scaling of size and duration, embedded in ceaseless timeseries of activity. Our analyses, confirmed by numerical simulation, suggest that inhibition may play a counterintuitive role in excitable networks.