✦ LIBER ✦

Integro-differential equations and the stability of neural networks with dendritic structure

✍ Scribed by Paul C. Bressloff

Book ID: 104661086
Publisher: Springer-Verlag
Year: 1995
Tongue: English
Weight: 900 KB
Volume: 73
Category: Article
ISSN: 0340-1200
DOI: 10.1007/bf00201430

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✦ Synopsis

We analyse the effects of dendritic structure on the stability of a recurrent neural network in terms of a set of coupled, non-linear Volterra integro-differential equations. These, which describe the dynamics of the somatic membrane potentials, are obtained by eliminating the dendritic potentials from the underlying compartmental model or cable equations. We then derive conditions for Turing-like instability as a precursor for pattern formation in a spatially organized network. These conditions depend on the spatial distribution of axo-dendritic connections across the network.

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