A timestepper-based approach for the coarse-grained analysis of microscopic neuronal simulators on networks: Bifurcation and rare-events micro- to macro-computations

Authors:
Konstantinos G. Spiliotis;Constantinos I. Siettos
Affiliations:
School of Applied Mathematics & Physical Sciences, National Technical University of Athens, Athens, GR-157 80, Greece;School of Applied Mathematics & Physical Sciences, National Technical University of Athens, Athens, GR-157 80, Greece
Venue:
Neurocomputing
Year:
2011

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Abstract

We show how the Equation Free approach for multi-scale computations can be exploited to extract, in a computational rigorous 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 bifurcation, stability analysis and estimation of mean appearance times of rare events can be derived bypassing the need for obtaining analytical approximations, providing an ''on-demand'' model reduction with respect to the underlying degree distribution.