EXISTENCE AND STABILITY OF LOCAL EXCITATIONS IN HOMOGENEOUS NEURAL FIELDS

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 function space. The dynamics of the field is in general multi-stable so that the field can keep short-term memory. © 1979 Springer-Verlag.