Critical Fluctuations and 1/f α-Activity of Neural Fields Involving Transmission Delays
A. Hutt
Institute of Physics, Humboldt University of Berlin, Newtonstr. 15, 12489 Berlin, Germany T. D. Frank
Institute for Theoretical Physics, University of Münster, Wilhelm-Klemm-Str. 9, 48149 Münster, Germany
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Received: 17 06 2005; in final form: 29 08 2005;
This work studies the stability and the stochastic properties of neural activity evoked by external stimulation. The underlying nonlocal model describes the spatiotemporal response dynamics of neural populations involving both synaptic delay and axonal transmission delay. We show that the linear model recasts to a set of affine 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 the case of external Gaussian noise. Further applications to specific kernels reveal critical fluctuations at Hopf- and Turing bifurcations and allow the numerical detection of 1/f αfluctuations near the stability threshold.
DOI: 10.12693/APhysPolA.108.1021
PACS numbers: 87.19.La, 05.40.Ca, 02.30.Ks, 05.70.Jk