Multiscale Computations on Neural Networks: From the Individual Neuron Interactions to the Macroscopic-Level Analysis

Abstract

We show how the Equation-Free approach for multi-scale 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 describing the evolving probability density function of the corresponding coarse-grained observables.

References in corpus (3)

• Weak pairwise correlations imply strongly correlated network states in a neural population
• Response of electrically coupled spiking neurons: a cellular automaton approach
• Coarse-graining the dynamics of coupled oscillators

Cited by in corpus (3)

• Equation-Free Multiscale Computational Analysis of Individual-Based Epidemic Dynamics on Networks
• Tuning the average path length of complex networks and its influence to the emergent dynamics of the majority-rule model
• Coarse-Grained Analysis of Microscopic Neuronal Simulators on Networks: Bifurcation and Rare-events computations