INTEGRODIFFERENTIAL EQUATIONS AND THE STABILITY OF NEURAL NETWORKS WITH DENDRITIC STRUCTURE

We analyse the effects of dendritic structure on the stability of a re current neural network in terms of a set of coupled, non-linear Volter ra integro-differential equations. These, which describe the dynamics of the somatic membrane potentials, are obtained by eliminating the de ndritic potentials from the underlying compartmental model or cable eq uations. We then derive conditions for Turing-like instability as a pr ecursor for pattern formation in a spatially organized network. These conditions depend on the spatial distribution of axo-dendritic connect ions across the network.