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.
Highlights
Synchronization is a well characterized phenomenon in natural systems [1]
The subsequent section shows the derivation of the mean-field equations, before they are applied to describe network dynamics for two types of partial stimulation
This study presents a rigorous derivation of mean-field equations for two nonlinearly coupled non-sparse Erdös-Rényi networks (ERN) that are stimulated by additive noise
Summary
Synchronization is a well characterized phenomenon in natural systems [1]. A confluence of experimental studies indicate that synchronization may be a hallmark pattern of selforganization [2,3,4]. While various mechanisms are possible, synchronization may emerge notably through an enhancement of internal interactions or via changes in external stimuli statistics. A specific type of synchronization can occur due to random external perturbations, leading to a noise-induced coherent activity. Such a phenomenon is called coherence resonance (CR) and has been found experimentally in solid states [5], nanotubes [6] and in neural systems [7, 8]. Theoretical descriptions of CR have been developed for single excitable elements [9, 9, 10], for excitable populations [11] and for clustered networks [12]
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