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Spontaneous and evoked activity in extended neural populations with gamma-distributed spatial interactions and transmission delay
Axel Hutt and Fatihcan M. Atay
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.