Spontaneous and evoked activity of synaptically coupled neuronal fields with axonal propagation delay for gamma-distributed connectivity kernels
Please always quote using this URN:urn:nbn:de:0296-matheon-426
- This work studies dynamical properties of spatially extended neu- ronal ensembles. We first derive an evolution equation from tem- poral properties and statistical distributions of synapses and somata. The obtained integro-differential equation considers both synaptic and axonal propagation delay, while spatial synaptic connectivities ex- hibit gamma-distributed distributions. This familiy of connectivity kernels also covers the cases of divergent, finite, and negligible self- connections. The work derives conditions for both stationary and nonstationary instabilities for gamma-distributed kernels.It turns out that the stability conditions can be formulated in terms of the mean spatial interaction ranges and the mean spatial interaction times. In addition, a numerical study examines the evoked spatiotemporal re- sponse activity caused by short local stimuli and reveals maximum response activity after the mean interaction time at a distance from stimulus offset location equal to the mean interaction range. These findings propose new insights to neuronal mechanisms of experimen- tally observed evoked brain activity.
Author: | Axel Hutt, Fatihcan M. Atay |
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URN: | urn:nbn:de:0296-matheon-426 |
Referee: | Anton Bovier |
Document Type: | Preprint, Research Center Matheon |
Language: | English |
Date of first Publication: | 2004/01/15 |
Release Date: | 2004/01/14 |
Institute: | Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS) |
Preprint Number: | 41 |