Clement Zankoc — Università degli Studi di Firenze - Department of Physics and SUPA and ICSMB - King's College - University of Aberdeen (UK) #
Fluctuating hydrodynamics approximation of the stochastic Cowan-Wilson model #
A stochastic version of the Wilson Cowan model is considered, which accommodates for a discrete
population of excitatory and inhibitory neurons. The model assumes a finite carrying capacity,
the two populations being hence constant in size. The master equation that governs the dynamics
of the stochastic model is expanded in powers of the inverse population size, yielding a coupled
pair of non linear Langevin equations with multiplicative noise. Numerical simulations point to
the validity of the obtained fluctuating hydrodynamics approximation, in the region of dynamical
bistability. Analytical progress is possible when silencing the retroaction of the activators on the
inhibitors, 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.