We consider a stochastic version of the Wilson–Cowan model which accommodates for discrete popula- tions of excitatory and inhibitory neurons. The model assumes a finite carrying capacity with the two populations being constant in size. The master equation that governs the dynamics of the stochastic model is analyzed by an expansion in powers of the inverse population size, yielding a coupled pair of non-linear Langevin equations with multiplicative noise. Gillespie simulations show the validity of the obtained approximation, for the parameter region where the system exhibits dynamical bistability. We report analytical progress by silencing the retroaction of excitatory neurons on inhibitory neurons, while still assigning the parameters so to fall in the region of deterministic bistability for the excitatory species. The proposed approach forms the basis of a perturbative generalization which applies to the case where a modest degree of coupling is restored.

Diffusion approximation of the stochastic Wilson-Cowan model / Zankoc, Clément; Biancalani, Tommaso; Fanelli, Duccio*; Livi, Roberto. - In: CHAOS, SOLITONS AND FRACTALS. - ISSN 0960-0779. - STAMPA. - 103:(2017), pp. 504-512. [10.1016/j.chaos.2017.07.010]

Diffusion approximation of the stochastic Wilson-Cowan model

Zankoc, Clément
;
Fanelli, Duccio
;
Livi, Roberto
2017

Abstract

We consider a stochastic version of the Wilson–Cowan model which accommodates for discrete popula- tions of excitatory and inhibitory neurons. The model assumes a finite carrying capacity with the two populations being constant in size. The master equation that governs the dynamics of the stochastic model is analyzed by an expansion in powers of the inverse population size, yielding a coupled pair of non-linear Langevin equations with multiplicative noise. Gillespie simulations show the validity of the obtained approximation, for the parameter region where the system exhibits dynamical bistability. We report analytical progress by silencing the retroaction of excitatory neurons on inhibitory neurons, while still assigning the parameters so to fall in the region of deterministic bistability for the excitatory species. The proposed approach forms the basis of a perturbative generalization which applies to the case where a modest degree of coupling is restored.
2017
103
504
512
Zankoc, Clément; Biancalani, Tommaso; Fanelli, Duccio*; Livi, Roberto
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1113186
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