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PubMed · 11561822

Circular stationary solutions in two-dimensional neural fields.

H Werner·T Richter
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Abstract

Stationary solutions are studied in two-dimensional homogeneous neural fields of the lateral-inhibition type. It is shown that in extending the one-dimensional theory to two dimensions, new phenomena arise. We discuss the conditions for the existence of localized solutions analogous to the one-dimensional theory and show that they are no longer sufficient in two dimensions. We give indications for the existence of mono- and bistable dynamics as known from the one-dimensional theory and, additionally, a tri-stable type of dynamic in two-dimensional neural fields, where, depending on the input, excitation dies out, spreads without limit, or causes a stable localized excitation.

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BrainHumansModels, NeurologicalNeural InhibitionNeuronsSensationJournal Article

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H Werner, T Richter. 2001. Circular stationary solutions in two-dimensional neural fields.. https://doi.org/10.1007/s004220000237

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