Spatial coherence resonance on diffusive and small-world networks of Hodgkin-Huxley neurons

TL;DR

This paper investigates how noise can induce spatial coherence resonance in Hodgkin-Huxley neuron networks and how network topology influences this phenomenon, showing that small-world links disrupt the resonance.

Contribution

It demonstrates the existence of spatial coherence resonance in diffusive Hodgkin-Huxley networks and reveals how small-world topology impairs this resonance.

Findings

Optimal noise intensity induces spatial coherence resonance in diffusive networks.

Small-world links rapidly destroy spatial coherence resonance.

Network topology critically affects noise-induced pattern formation.

Abstract

Spatial coherence resonance in a spatially extended system that is locally modeled by Hodgkin-Huxley (HH) neurons is studied in this paper. We focus on the ability of additive temporally and spatially uncorrelated Gaussian noise to extract a particular spatial frequency of excitatory waves in the medium, whereby examining also the impact of diffusive and small-world network topology determining the interactions amongst coupled HH neurons. We show that there exists an intermediate noise intensity that is able to extract a characteristic spatial frequency of the system in a resonant manner provided the latter is diffusively coupled, thus indicating the existence of spatial coherence resonance. However, as the diffusive topology of the medium is relaxed via the introduction of shortcut links introducing small-world properties amongst coupled HH neurons, the ability of additive Gaussian noise to evoke ordered excitatory waves deteriorates rather spectacularly, leading to the decoherence of the spatial dynamics and with it related absence of spatial coherence resonance. In particular, already a minute fraction of shortcut links suffices to substantially disrupt coherent pattern formation in the examined system.