Stability, critical fluctuations and $1/f^\\alpha$-activity of neural fields involving transmission delays
Please always quote using this URN:urn:nbn:de:0296-matheon-1509
- This work studies the stability and the stochastic properties of neural activity evoked by external stimulation. The underlying model describes the spatiotemporal dynamics of neural populations involving both synaptic delay and axonal transmission delay. We show, that the linear model recasts to a set of affne delay differential equations in spatial Fourier space. Besides a stability study for general kernels and general external stimulation, the power spectrum of evoked activity is derived analytically in case of external Gaussian noise. Further applications to specific kernels reveal critical uctuations at Hopf- and Turing bifurcations and allow the numerical detection of 1/f fluctuations near the stability threshold.
Author: | Axel Hutt, Till Frank |
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URN: | urn:nbn:de:0296-matheon-1509 |
Referee: | Anton Bovier |
Document Type: | Preprint, Research Center Matheon |
Language: | English |
Date of first Publication: | 2004/07/15 |
Release Date: | 2004/07/15 |
Institute: | Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS) |
Preprint Number: | 140 |