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Population and Subpopulation Models

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Stochastic Neuron Models

Part of the book series: Mathematical Biosciences Institute Lecture Series ((STOCHBS,volume 1.5))

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Abstract

We have seen stochastic neuron firing models that have inherent frequencies in their subthreshold dynamics, e.g., for the Morris-Lecar neuron [28]. This frequency shows up at the population level. If we record the firings of several model neurons over a period of time, the firings of each single neuron follow an inherent frequency, but often skipping many repeats of that frequency. The skipping phenomenon is a result of the tendency of the neurons to fire on their subthreshold quasicycles, a stochastic facilitation phenomenon explained in Sections 1.2 and 2.5 When the firings of the several neurons, driven by the same or partially common noise, are added together as a function of time, we obtain a function that oscillates at the common inherent frequency of the family.

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Authors and Affiliations

  1. University of British Columbia, Vancouver, Canada

    Priscilla E. Greenwood & Lawrence M. Ward

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  1. Priscilla E. Greenwood
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  2. Lawrence M. Ward
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Greenwood, P.E., Ward, L.M. (2016). Population and Subpopulation Models. In: Stochastic Neuron Models. Mathematical Biosciences Institute Lecture Series(), vol 1.5. Springer, Cham. https://doi.org/10.1007/978-3-319-26911-5_3

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