Diffusion approximation of the stochastic Wilson-Cowan model

作者：Zankoc Clement; Biancalani Tommaso; Fanelli Duccio^*; Livi Roberto

来源：Chaos Solitons & Fractals, 2017, 103: 504-512.

DOI：10.1016/j.chaos.2017.07.010

• Stochastic models
• Bistability
• Kramers Moyal
• Neuronal dynamics

We consider a stochastic version of the Wilson-Cowan model which accommodates for discrete populations 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.

• 出版日期2017-10
• 单位MIT