Analysis of nonlocal neural fields for both general and gamma-distributed connectivities
Please always quote using this URN:urn:nbn:de:0296-matheon-1444
- This work studies the stability of spatially extended neuronal ensembles. We first derive the model equation from statistical properties of the neuron population. The obtained integro-differential equation considers synaptic and space-dependent transmission delay for both general and gamma-distributed synaptic connectivities. The latter connectivity type reveals infinite, finite and vanishing self-connectivities. The work derives conditions for stationary and nonstationary instabilities for both kernel types. In addition, a nonlinear analysis for general kernels yields the order parameter equation of the Turing instability. To compare the results to findings for partial differential equations (PDEs), two typical PDE-types are derived from the examined model equation. In case of the gamma-distributed kernels, the stability conditions are formulated in terms of the mean excitatory and inhibitory interaction ranges. As a novel finding, we obtain Turing instabilities in fields with local inhibition-lateral excitation, while wave instabilities occur in fields with local excitation and lateral inhibition. Numerical simulations support the analytical results.
Author: | Axel Hutt, Fatihcan M. Atay |
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URN: | urn:nbn:de:0296-matheon-1444 |
Referee: | Anton Bovier |
Document Type: | Preprint, Research Center Matheon |
Language: | English |
Date of first Publication: | 2004/02/06 |
Release Date: | 2004/01/06 |
Preprint Number: | 132 |