Generalized Wilson-Cowan rate equations for correlated activity in neural networks.
The Wilson-Cowan equations are the foundation of a common approach to modeling for neural networks. These equations provide dynamics for the firing rate of neurons within a network given some connectivity. The shortcoming of these equations is that they take into account only the average firing rate while leaving out higher order statistics like correlations between firing. Recently, Buice and Cowan formulated a stochastic theory of neural networks which includes statistics at all orders. We describe how this theory yields a systematic extension to the Wilson-Cowan equations by introducing equations for correlations and appropriate coupling terms. Each level of the approximation yields closed equations, i.e. they depend only upon the mean and specific correlations of interest, without an ad hoc criterion for doing so. In addition to presenting the evolution equations for the mean activity and correlations, we solve them for the simple case of a homogeneous all-to-all connected network and compare the results to simulations of a network of integrate-and-fire neurons.
Conference:
Computational and systems
neuroscience 2009, Salt Lake City, UT, United States, 26 Feb - 3 Mar, 2009.
Presentation Type:
Poster Presentation
Topic:
Poster Presentations
Citation:
(2009). Generalized Wilson-Cowan rate equations for correlated activity in neural networks..
Front. Syst. Neurosci.
Conference Abstract:
Computational and systems
neuroscience 2009.
doi: 10.3389/conf.neuro.06.2009.03.078
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Received:
30 Jan 2009;
Published Online:
30 Jan 2009.