Abstract
We present here a method for the study of stochastic neurodynamics in the master equation framework. Our aim is to obtain a statistical description of the dynamics of fluctuations and correlations of neural activity in large neural networks. We focus on a macroscopic description of the network via a master equation for the number of active neurons in the network. We present a systematic expansion of this equation using the “system size expansion”. We obtain coupled dynamical equations for the average activity and of fluctuations around this average. These equations exhibit non-monotonic approaches to equilibrium, as seen in Monte Carlo simulations.
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© 1997 Springer Science+Business Media New York
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Ohira, T., Cowan, J.D. (1997). Stochastic Neurodynamics and the System Size Expansion. In: Ellacott, S.W., Mason, J.C., Anderson, I.J. (eds) Mathematics of Neural Networks. Operations Research/Computer Science Interfaces Series, vol 8. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-6099-9_50
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DOI: https://doi.org/10.1007/978-1-4615-6099-9_50
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