2024/08/22 by Daniele Avitabile, Avitabile, Daniele, James MacLaurin +1 · 1 citation
Computer Science · #Dynamical Systems (math.DS) #FOS: Biological sciences #FOS: Mathematics #Neural Networks and Applications #Neurons and Cognition (q-bio.NC) #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2408.12540
openalex publication_date 2024/08/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study pattern formation in class of a large-dimensional neural networks posed on random graphs and subject to spatio-temporal stochastic forcing. Under generic conditions on coupling and nodal dynamics, we prove that the network admits a rigorous mean-field limit, resembling a Wilson-Cowan neural field equation. The state variables of the limiting systems are the mean and variance of neuronal activity. We select networks whose mean-field equations are tractable and we perform a bifurcation analysis using as control parameter the diffusivity strength of the afferent white noise on each neuron. We find conditions for Turing-like bifurcations in a system where the cortex is modelled as a ring, and we produce numerical evidence of noise-induced spiral waves in models with a two-dimensional cortex. We provide numerical evidence that solutions of the finite-size network converge weakly to solutions of the mean-field model. Finally, we prove a Large Deviation Principle, which provides a means of assessing the likelihood of deviations from the mean-field equations induced by finite-size effects.