Title of article :
Mean-field equations for stochastic firing-rate neural fields with delays: Derivation and noise-induced transitions
Author/Authors :
Touboul، نويسنده , , Jonathan، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2012
Pages :
22
From page :
1223
To page :
1244
Abstract :
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.
Keywords :
Collective dynamics , Noise , neural fields , Turing instabilities , bifurcations
Journal title :
Physica D Nonlinear Phenomena
Serial Year :
2012
Journal title :
Physica D Nonlinear Phenomena
Record number :
1730159
Link To Document :
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