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
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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Further Reading
Ben-Yishai R, Bar-Or L, Sompolinsky H (1995) Theory of orientation tuning in visual cortex. Proc Natl Acad Sci U S A 92:3844–3848
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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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Amari Model- Published:
- 07 August 2014
DOI: https://doi.org/10.1007/978-1-4614-7320-6_51-2
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The Amari Model in Neural Field Theory- Published:
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DOI: https://doi.org/10.1007/978-1-4614-7320-6_51-1