Abstract
Chapter describes the construction of population-based rate models under the assumption that the spiking of individual neurons is unimportant. The issue of how stochasticity at the single-cell level manifests itself at the population level is discussed, introducing topics such as balanced networks, Poisson statistics, and asynchronous states. Stochastic methods are then used to analyze bistability in a stochastic population model. Finally, the transition from spatially structured neural networks to continuum neural fields is highlighted. The latter take the form of nonlocal integrodifferential equations, in which the integral kernel represents the distribution of synaptic connections.
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Bressloff, P.C. (2014). Population Models and Neural Fields. In: Waves in Neural Media. Lecture Notes on Mathematical Modelling in the Life Sciences. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8866-8_6
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