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Amari Model

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Encyclopedia of Computational Neuroscience

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Definition

The Amari neural field model (cf. (Amari 1975, 1977)) provides a simple field-theoretic approach to the dynamics of neural activity in the brain. The model uses excitations and inhibitions over some distance as an effective model of mixed inhibitory and excitatory neurons with typical cortical connectivities. The model is a scalar dynamical equation for the voltage or activity u(x, t) of the form

$$ \frac{\partial u}{\partial t}\;\left(x,t\right)=-u\left(x,t\right)+{\displaystyle {\int}_Bw\left(x,y\right)\;f\left(u\left(y,t\right)\right) dy,\kern0.48em x\in B,t\ge 0,} $$
(1)

where initial conditions u(x,0) = u 0(x), x ∈ B are given. Here, B is our brain, i.e., some domain where the neural activity takes place; f is the local activation function or firing rate function; and w is the connectivity function which models the strength of the connectivity or signal propagation from y ∈ B to the point x.

A common choice for the activation function has sigmoidal shape

$$...

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Authors and Affiliations

  1. Department of Mathematics, University of Reading, Reading, PO Box 220, South East England, UK

    Prof. Roland Potthast

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  1. Prof. Roland Potthast
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Correspondence to Roland Potthast .

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Editors and Affiliations

  1. Atlanta, Georgia, USA

    Dieter Jaeger

  2. Department of Biomedical Engineering, Florida International University, Miami, Florida, USA

    Ranu Jung

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Potthast, R. (2014). Amari Model. In: Jaeger, D., Jung, R. (eds) Encyclopedia of Computational Neuroscience. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7320-6_51-2

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  • DOI: https://doi.org/10.1007/978-1-4614-7320-6_51-2

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Chapter history

  1. Latest

    Amari Model
    Published:
    07 August 2014

    DOI: https://doi.org/10.1007/978-1-4614-7320-6_51-2

  2. Original

    The Amari Model in Neural Field Theory
    Published:
    07 February 2014

    DOI: https://doi.org/10.1007/978-1-4614-7320-6_51-1

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