MULTISCALE COMPUTATIONS ON NEURAL NETWORKS: FROM THE INDIVIDUAL NEURON INTERACTIONS TO THE MACROSCOPIC-LEVEL ANALYSIS

Abstract

We show how the Equation-Free approach for multiscale computations can be exploited to systematically study the dynamics of neural interactions on a random regular connected graph under a pairwise representation perspective. Using an individual-based microscopic simulator as a black box coarse-grained timestepper and with the aid of Simulated Annealing we compute the coarse-grained equilibrium bifurcation diagram and analyze the stability of the stationary states, sidestepping the necessity of obtaining explicit closures at the macroscopic level. We also exploit the scheme to perform a rare-events analysis by estimating an effective Fokker–Planck equation describing the evolving probability density function of the corresponding coarse-grained observables.