McKean-Vlasov Equations for Large Networks of Neurons with Adaptive Asymmetric Edges

Authors

Avitabile D., MacLaurin J.

Abstract

Classical McKean-Vlasov theory concerns high-dimensional particle systems for which the effect of one particle on another is instantaneous. However in many applications, particularly neuroscience, the effect of one particle on another is not instantaneous but delayed. For biophysically-accurate neuroscientific models, for each j ↦ k connection one can introduce an additional stochastic process that describes the propagation of the signal from j to k. In this paper we determine a self-consistent autonomous SDE that describes the high-dimensional limit of such neural networks. We apply this system to a model of the visual cortex from mathematical neuroscience. We determine the existence of spatio-temporal oscillations in the average neural activity.

Links

PDF Arxiv

BibTeX

@misc{avitabile2026mckean,
  author        = {Avitabile, Daniele and MacLaurin, James},
  title         = {McKean-Vlasov Equations for Large Networks of Neurons with Adaptive Asymmetric Edges},
  year          = {2026},
  eprint        = {2606.21394},
  archiveprefix = {arXiv},
  primaryclass  = {math.PR},
  doi           = {10.48550/arXiv.2606.21394}
}