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Neural field equations are used to describe the spatiotemporal evolution ofthe activity in a network of synaptically coupled populations of neurons in thecontinuum limit. Their heuristic derivation involves two approximation steps.Under the assumption that each population in the network is large, the activityis described in terms of a population average. The discrete network is thenapproximated by a continuum. In this article we make the two approximationsteps explicit. Extending a model by Bressloff and Newby, we describe theevolution of the activity in a discrete network of finite populations by aMarkov chain. In order to determine finite-size effects - deviations from themean field limit due to the finite size of the populations in the network - weanalyze the fluctuations of this Markov chain and set up an approximatingsystem of diffusion processes. We show that a well-posed stochastic neuralfield equation with a noise term accounting for finite-size effects ontraveling wave solutions is obtained as the strong continuum limit.

Finite-Size Effects on Traveling Wave Solutions to Neural Field Equations