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 fuction space. The dynamcis of the field is in general multi-stable so that the field can keep short-term memory.
D006801:Humans; D008433:Mathematics; D008564:Membrane Potentials; D008959:Models, Neurological; D009433:Neural Inhibition; D009474:Neurons / Q000502:physiology*; D009435:Synaptic Transmission