Periodically-forced finite networks of heterogeneous globally-coupled oscillators: A low-dimensional approach

Carlo R. Laing, Ioannis G. Kevrekidis

Research output: Contribution to journalArticle

13 Scopus citations

Abstract

We study a network of 500 globally-coupled modified van der Pol oscillators. The value of a parameter associated with each oscillator is drawn from a normal distribution, giving a heterogeneous network. For strong enough coupling the oscillators all have the same period, and we consider periodic forcing of the network when it is in this state. By exploiting the correlations that quickly develop between the state of an oscillator and the value of its parameter we obtain an approximate low-dimensional description of the system in terms of the first few coefficients in a polynomial chaos expansion. Standard bifurcation analysis can then be performed on the low-dimensional system which results from this computational coarse-graining, and the results obtained from this predict very well the behaviour of the high-dimensional system for any set of realisations of the random parameter. Situations in which the method begins to fail are also discussed.

Original languageEnglish (US)
Pages (from-to)207-215
Number of pages9
JournalPhysica D: Nonlinear Phenomena
Volume237
Issue number2
DOIs
StatePublished - Feb 2008

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics

Keywords

  • Bifurcation
  • Coupled oscillators
  • Equation-free
  • Polynomial chaos

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