Applied & Computational Mathematics seminar: Pattern Formation and Noise-Induced Transitions in High Dimensional Inhomogeneous Neural Networks

Speaker: James MacLaurin, NJIT

Title:  Pattern Formation and Noise-Induced Transitions in High Dimensional Inhomogeneous Neural Networks

Abstract:  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. 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. The joint effects of clustering / spatial structure of the connectivity on pattern formation is also explored. Finally, we compute the most likely transitions paths between attractors induced by finite-size effects by proving a Large Deviation Principle and using this to compute the most likely transition path. Most of this work is joint with Daniele Avitabile.

Time:  Friday, October 18 – 1:30pm – 2:30pm
Place:  Exploratory Hall, room 4106 and Zoom