

Preprint 91/2003
Spontaneous and evoked activity in extended neural populations with gamma-distributed spatial interactions and transmission delay
Axel Hutt and Fatihcan M. Atay
Contact the author: Please use for correspondence this email.
Submission date: 06. Nov. 2003 (revised version: January 2006)
published in: Chaos, solitons and fractals, 32 (2007) 2, p. 547-560
DOI number (of the published article): 10.1016/j.chaos.2005.10.091
Bibtex
PACS-Numbers: 02.30.Rz, 87.18.Hf
Keywords and phrases: neuronal ensemble, synaptic connectivity kernel, bifurcation, stimulus response
Abstract:
This work studies dynamical properties of spatially extended neuronal ensembles.
We first derive an evolution equation from temporal properties and statistical
distributions of synapses and somata. The obtained integro-differential equation
considers both synaptic and axonal propagation delay, while spatial synaptic
connectivities exhibit 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 response 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 experimentally observed evoked brain activity.