Coarse graining the dynamics of heterogeneous oscillators in networks with spectral gaps

Karthikeyan Rajendran, Ioannis G. Kevrekidis

Research output: Contribution to journalArticle

8 Scopus citations

Abstract

We present a computer-assisted approach to coarse graining the evolutionary dynamics of a system of nonidentical oscillators coupled through a (fixed) network structure. The existence of a spectral gap for the coupling network graph Laplacian suggests that the graph dynamics may quickly become low dimensional. Our first choice of coarse variables consists of the components of the oscillator states-their (complex) phase angles-along the leading eigenvectors of this Laplacian. We then use the equation-free framework, circumventing the derivation of explicit coarse-grained equations, to perform computational tasks such as coarse projective integration, coarse fixed-point, and coarse limit-cycle computations. In a second step, we explore an approach to incorporating oscillator heterogeneity in the coarse-graining process. The approach is based on the observation of fast-developing correlations between oscillator state and oscillator intrinsic properties and establishes a connection with tools developed in the context of uncertainty quantification.

Original languageEnglish (US)
Article number036708
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume84
Issue number3
DOIs
StatePublished - Sep 21 2011

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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