Mean-field equations for stochastic firing-rate neural fields with delays: Derivation and noise-induced transitions

PHYSICA D-NONLINEAR PHENOMENA

卷:241

Article

Touboul, Jonathan^1,2 

[1] UPMC, Math Neurosci Lab, CNRS UMR 7241,ED 158, Coll France,CIRB,MEMOLIFE PSL,INSERM,U1050, F-75005 Paris, France

[2] INRIA Paris, BANG Lab, F-75005 Paris, France

关键词: Noise;    Neural fields;    Collective dynamics;    Bifurcations;    Turing instabilities;   

DOI  :  10.1016/j.physd.2012.03.010

来源: Elsevier

【 摘 要 】

In this manuscript we analyze the collective behavior of mean-field limits of large-scale, spatially extended stochastic neuronal networks with delays. Rigorously, the asymptotic regime of such systems is characterized by a very intricate stochastic delayed integro-differential McKean-Vlasov equation that remain impenetrable, leaving the stochastic collective dynamics of such networks poorly understood. In order to study these macroscopic dynamics, we analyze networks of firing-rate neurons, i.e. with linear intrinsic dynamics and sigmoidal interactions. In that case, we prove that the solution of the mean-field equation is Gaussian, hence characterized by its two first moments, and that these two quantities satisfy a set of coupled delayed integro-differential equations. These equations are similar to usual neural field equations, and incorporate noise levels as a parameter, allowing analysis of noise-induced transitions. We identify through bifurcation analysis several qualitative transitions due to noise in the mean-field limit. In particular, stabilization of spatially homogeneous solutions, synchronized oscillations, bumps, chaotic dynamics, wave or bump splitting are exhibited and arise from static or dynamic Turing-Hopf bifurcations. These surprising phenomena allow further exploring the role of noise in the nervous system. (C) 2012 Elsevier B.V. All rights reserved.

【 授权许可】

Free