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. 1979 May 15;7(4):303-18.
doi: 10.1007/BF00275151.

Existence and stability of local excitations in homogeneous neural fields

K Kishimoto, S Amari

Existence and stability of local excitations in homogeneous neural fields

K Kishimoto et al. J Math Biol. .

Abstract

Dynamics of excitation patterns is studied in one-dimensional homogeneous lateral-inhibition type neural fields. The existence of a local excitation pattern solution as well as its waveform stability is proved by the use of the Schauder fixed-point theorem and a generalized version of the Perron-Frobenius theorem of positive matrices to the fuction space. The dynamcis of the field is in general multi-stable so that the field can keep short-term memory.

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