Cellular-Automata-Like Simulations Of Dynamic Neural Fields

This paper is motivated by two aims. Firstly, we want to describe a method for simulations of two-dimensional DNFs and secondly, we show their use to two dierent problems in computational neuroscience. Amari (Amari, 1977) investigated a model of DNFs as a set of IDEs and found solutions for the one-dimensional spatial case. However, most spatio-temporal computations of mammalian brains involve more than one spatial dimension. Therefore we present a method to simulate two-dimensional DNFs which is based on cellular automata (CA) simulations as used for reaction-diusion systems. The simulations oer a powerful way to investigate qualitatively the dynamics of the spatio-temporal patterns described by the IDEs. Further they can be used in applications employing biologically motivated space-time computations. In the next section we look shortly at the results of Amari's work. Then we give details of our own simulations for two-dimensional DNFs. In Section 4 we discuss the usefulness of our method. In Section 5 we exemplify the approach by applying it to two problems in computational neuroscience. The last section ends with some conclusions. 2 DYNAMIC NEURAL FIELD