Coarse-Grained Analysis of Microscopic Neuronal Simulators on Networks: Bifurcation and Rare-events computations

TL;DR

This paper demonstrates how the Equation-Free multiscale approach can systematically analyze emergent dynamics, bifurcations, and rare events in large-scale stochastic neuronal network models without requiring explicit analytical solutions.

Contribution

It introduces a systematic, computationally strict method to extract macroscopic dynamical features from microscopic neuronal network simulations using the Equation-Free framework.

Findings

Computed coarse-grained bifurcation diagrams for neuronal networks.

Analyzed stability of emergent solutions in network models.

Estimated mean occurrence times of rare events based on network topology.

Abstract

We show how the Equation-Free approach for mutliscale computations can be exploited to extract, in a computational strict and systematic way the emergent dynamical attributes, from detailed large-scale microscopic stochastic models, of neurons that interact on complex networks. In particular we show how the Equation-Free approach can be exploited to perform system-level tasks such as bifurcation, stability analysis and estimation of mean appearance times of rare events, bypassing the need for obtaining analytical approximations, providing an "on-demand" model reduction. Using the detailed simulator as a black-box timestepper, we compute the coarse-grained equilibrium bifurcation diagrams, examine the stability of the solution branches and perform a rare-events analysis with respect to certain characteristics of the underlying network topology such as the connectivity degree