2009/02/23 by Michael A. Buice, Buice, Michael A., Jack D. Cowan +3 · 1 citation
Computer Science · Neuroscience · #FOS: Biological sciences #Neural Networks and Applications #Neural dynamics and brain function #Neurons and Cognition (q-bio.NC) #Nonlinear Dynamics and Pattern Formation
paper · pdf · doi:10.48550/arxiv.0902.3925
openalex publication_date 2009/02/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Population rate or activity equations are the foundation of a common approach to modeling for neural networks. These equations provide mean field dynamics for the firing rate or activity 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. A stochastic theory of neural networks which includes statistics at all orders was recently formulated. We describe how this theory yields a systematic extension to population rate 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 \it ad hoc criterion for doing so. We show in an example of an all-to-all connected network how our system of generalized activity equations captures phenomena missed by the mean fieldrate equations alone.