Effective bifurcation analysis: A time-stepper-based approach

Olof Runborg, Constantinos Theodoropoulos, Ioannis G. Kevrekidis

Research output: Contribution to journalArticle

60 Scopus citations

Abstract

We introduce a numerical approach to perform the effective (coarse-scale) bifurcation analysis of solutions of dissipative evolution equations with spatially varying coefficients. The advantage of this approach is that the 'coarse model' (the averaged, effective equation) need not be explicitly constructed. The method only uses a time-integrator code for the detailed problem and judicious choices of initial data and integration times; the bifurcation computations are based on the so-called recursive projection method (Shroff and Keller 1993 SIAM J. Numer. Anal. 30 1099-120).

Original languageEnglish (US)
Pages (from-to)491-511
Number of pages21
JournalNonlinearity
Volume15
Issue number2
DOIs
StatePublished - Mar 1 2002

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

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    Runborg, O., Theodoropoulos, C., & Kevrekidis, I. G. (2002). Effective bifurcation analysis: A time-stepper-based approach. Nonlinearity, 15(2), 491-511. https://doi.org/10.1088/0951-7715/15/2/314