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

Frontiers in Applied Mathematics and Statistics

J. Lefebvre¹  N. Voges²  Jo Hausmann³  T. Wahl⁴  A. Hutt⁴ 

[1]D Department, Hyland Switzerland Sarl, Geneva, Switzerland

[2]ILCB and INT UMR 7289, Aix Marseille Université, Marseille, France

[3]

[4]R&Team MIMESIS, INRIA Nancy Grand Est, Strasbourg, France

关键词: coherence resonance;    phase transition;    stochastic process;    excitable system;    mean-field;    random networks;   

DOI  :  10.3389/fams.2021.697904

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown