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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Received: 19 July 2000 / Accepted in revised form: 18 December 2000
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Werner, H., Richter, T. Circular stationary solutions in two-dimensional neural fields. Biol Cybern 85, 211–217 (2001). https://doi.org/10.1007/s004220000237
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DOI: https://doi.org/10.1007/s004220000237