Local excitation solutions in one-dimensional neural fields by external input stimuli

Large deviations for nonlocal stochastic neural fields

We study the effect of additive noise on integro-differential neural field equations. In particular, we analyze an Amari-type model driven by a Q-Wiener process, and focus on noise-induced transitions and escape. We argue that proving a sharp Kramers' law for neural fields poses substantial difficulties, but that one may transfer techniques from stochastic partial differential equations to establish a large deviation principle (LDP). Then we demonstrate that an efficient finite-dimensional approximation of the stochastic neural field equation can be achieved using a Galerkin method and that the resulting finite-dimensional rate function for the LDP can have a multiscale structure in certain cases. These results form the starting point for an efficient practical computation of the LDP. Our approach also provides the technical basis for further rigorous study of noise-induced transitions in neural fields based on Galerkin approximations.Mathematics Subject Classification (2000): 60F10, 60H15, 65M60, 92C20.

A New Clustering Approach on the Basis of Dynamical Neural Field

In this letter, we present a new hierarchical clustering approach based on the evolutionary process of Amari's dynamical neural field model. Dynamical neural field theory provides a theoretical framework macroscopically describing the activity of neuron ensemble. Based on it, our clustering approach is essentially close to the neurophysiological nature of perception. It is also computationally stable, insensitive to noise, flexible, and tractable for data with complex structure. Some examples are given to show the feasibility.