Existence and properties of stationary solution of dynamical neural field

In this paper, we discuss the existence and properties of stationary solution of Amari’s dynamical neural field model in RnRn. Amari’s model has been extensively applied in psychophysics, neurophysiology, machine vision and cognition, where its stationary solution plays an important role. Though many problems in these applications are presented in high dimensional spaces, most investigations on the stationary solutions of neural field are in RR and R2R2. Under certain general assumptions on neural field, we obtain some existence conditions for general stationary solution, as well as some typical stationary solutions. Some results on their stabilities are also obtained.