Stability and Bifurcations in Neural Fields with Axonal Delay and General Connectivity
Please always quote using this URN:urn:nbn:de:0296-matheon-415
- A stability analysis is presented for neural field equations in the presence of axonal delays and for a general class of connectivity kernels and synap- tic properties. Sufficient conditions are given for the stability of equilibrium solutions. It is shown that the delays play a crucial role in non-stationary bifurcations of equilibria, whereas the stationary bifurcations depend only on the kernel. Bounds are determined for the frequencies of bifurcating periodic solutions. A perturbative scheme is used to calculate the types of bifurca- tions leading to spatial patterns, oscillatory solutions, and traveling waves. For high transmission speeds a simple method is derived that allows the de- termination of the bifurcation type by visual inspection of the Fourier trans- forms of the connectivity kernel and its first moment. Results are numerically illustrated on a class of neurologically plausible second order systems with combinations of Gaussian excitatory and inhibitory connections.
Author: | Fatihcan M. Atay, Axel Hutt |
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URN: | urn:nbn:de:0296-matheon-415 |
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: | 40 |