2010/01/21 by Jonathan Touboul, Bard Ermentrout, Touboul, Jonathan +5
Computer Science · Neuroscience · Physics and Astronomy · #FOS: Biological sciences #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Neural Networks and Applications #Neural dynamics and brain function #Neurons and Cognition (q-bio.NC) #Probability (math.PR) #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.1001.3872
openalex publication_date 2010/01/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We review a recent approach to the mean-field limits in neural networks that takes into account the stochastic nature of input current and the uncertainty in synaptic coupling. This approach was proved to be a rigorous limit of the network equations in a general setting, and we express here the results in a more customary and simpler framework. We propose a heuristic argument to derive these equations providing a more intuitive understanding of their origin. These equations are characterized by a strong coupling between the different moments of the solutions. We analyse the equations, present an algorithm to simulate the solutions of these mean-field equations, and investigate numerically the equations. In particular, we build a bridge between these equations and Sompolinsky and collaborators approach (1988, 1990), and show how the coupling between the mean and the covariance function deviates from customary approaches.