Inhibition causes ceaseless dynamics in networks of excitable nodes

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.

11 pages, 6 figures

References in corpus (8)

• Power-law distributions in empirical data
• Competing epidemics on complex networks
• Spike Avalanches Exhibit Universal Dynamics across the Sleep-Wake Cycle
• Approximating the largest eigenvalue of network adjacency matrices
• Statistical Properties of Avalanches in Networks
• Effects of network topology, transmission delays, and refractoriness on the response of coupled excitable systems to a stochastic stimulus
• How to enhance the dynamic range of excitatory-inhibitory excitable networks
• Signal integration enhances the dynamic range in neuronal systems

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