Coherence Resonance in Random Erdös-Rényi Neural Networks: Mean-Field Theory

Hutt, A. and Wahl, T. and Voges, N. and Hausmann, Jo and Lefebvre, J. (2021) Coherence Resonance in Random Erdös-Rényi Neural Networks: Mean-Field Theory. Frontiers in Applied Mathematics and Statistics, 7. ISSN 2297-4687

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Abstract

Additive noise is known to tune the stability of nonlinear systems. Using a network of two randomly connected interacting excitatory and inhibitory neural populations driven by additive noise, we derive a closed mean-field representation that captures the global network dynamics. Building on the spectral properties of Erdös-Rényi networks, mean-field dynamics are obtained via a projection of the network dynamics onto the random network’s principal eigenmode. We consider Gaussian zero-mean and Poisson-like noise stimuli to excitatory neurons and show that these noise types induce coherence resonance. Specifically, the stochastic stimulation induces coherent stochastic oscillations in the γ-frequency range at intermediate noise intensity. We further show that this is valid for both global stimulation and partial stimulation, i.e. whenever a subset of excitatory neurons is stimulated only. The mean-field dynamics exposes the coherence resonance dynamics in the γ-range by a transition from a stable non-oscillatory equilibrium to an oscillatory equilibrium via a saddle-node bifurcation. We evaluate the transition between non-coherent and coherent state by various power spectra, Spike Field Coherence and information-theoretic measures.

Item Type: Article
Subjects: European Repository > Mathematical Science
Depositing User: Managing Editor
Date Deposited: 04 Jan 2023 05:00
Last Modified: 16 Sep 2023 04:04
URI: http://go7publish.com/id/eprint/1233

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