Dynamics of pattern formation in lateral-inhibition type neural fields

The dynamics of pattern formation is studied for lateral-inhibition type homogeneous neural fields with general connections. Neural fields consisting of single layer are first treated, and it is proved that there are five types of pattern dynamics. The type of the dynamics of a field depends not only on the mutual connections within the field but on the level of homogeneous stimulus given to the field. An example of the dynamics is as follows: A fixed size of localized excitation, once evoked by stimulation, can be retained in the field persistently even after the stimulation vanishes. It moves until it finds the position of the maximum of the input stimulus. Fields consisting of an excitatory and an inhibitory layer are next analyzed. In addition to stationary localized excitation, fields have such pattern dynamics as production of oscillatory waves, travelling waves, active and dual active transients, etc.