Equation-free analysis of a dynamically evolving multigraph

A. Holiday, I. G. Kevrekidis

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


In order to illustrate the adaptation of traditional continuum numerical techniques to the study of complex network systems, we use the equation-free framework to analyze a dynamically evolving multigraph. This approach is based on coupling short intervals of direct dynamic network simulation with appropriately-defined lifting and restriction operators, mapping the detailed network description to suitable macroscopic (coarse-grained) variables and back. This enables the acceleration of direct simulations through Coarse Projective Integration (CPI), as well as the identification of coarse stationary states via a Newton-GMRES method. We also demonstrate the use of data-mining, both linear (principal component analysis, PCA) and nonlinear (diffusion maps, DMAPS) to determine good macroscopic variables (observables) through which one can coarse-grain the model. These results suggest methods for decreasing simulation times of dynamic real-world systems such as epidemiological network models. Additionally, the data-mining techniques could be applied to a diverse class of problems to search for a succint, low-dimensional description of the system in a small number of variables.

Original languageEnglish (US)
Pages (from-to)1281-1292
Number of pages12
JournalEuropean Physical Journal: Special Topics
Issue number6-7
StatePublished - Sep 1 2016

All Science Journal Classification (ASJC) codes

  • General Materials Science
  • General Physics and Astronomy
  • Physical and Theoretical Chemistry


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