Neural pattern formation in networks with dendritic structure

• Published in: Physica. D 1998, Vol.115 (1), p.124-144
• Main Authors: Bressloff, P.C., De Souza, B.
• Format: Article
• Language: English
• ISSN: 0167-2789; 1872-8022
• DOI: 10.1016/S0167-2789(97)00231-5

We present a detailed analysis of a recently proposed model of neural pattern formation that is based on the combined effect of diffusion along a neuron's dendritic tree and recurrent interactions along axo-dendritic synaptic connections. For concreteness, we consider a one-dimensional array of analog neurons with the dendritic tree idealized as a one-dimensional cable. Linear stability analysis and bifurcation theory together with numerical simulations are used to establish conditions for the onset of a Turing instability leading to the formation of stable spatial patterns of network output activity. It is shown that the presence of dendritic structure can induce dynamic (time-periodic) spatial pattern formation. Moreover, correlations between the dendritic location of a synapse and the relative positions of neurons in the network are shown to result in spatially oscillating patterns of activity along the dendrites of each neuron.