A convergence-improving iterative method for computing periodic orbits near Bifurcation Points

Michael N. Vrahatis, Tassos Bountis, Nurit Budinsky

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

The accurate computation of periodic orbits and the precise knowledge of their bifurcation properties are very important for studying the behavior of many dynamical systems of physical interest. In this paper, we present an iterative method for computing periodic orbits, which has the advantage of improving the convergence of previous Newton-like schemes, especially near bifurcation points. This method is illustrated here on a conservative, nonlinear Mathieu equation, for which a sequence of period-doubling bifurcations is followed, long enough to obtain accurate estimates of the two universal scaling constants α, β, as well as the universal rate δ, by which the bifurcation values of a parameter q = qk, k =1, 2, 3, ..., tend to their limiting value, q < ∞, as k increases.

Original languageEnglish
Pages (from-to)1-14
Number of pages14
JournalJournal of Computational Physics
Volume88
Issue number1
DOIs
Publication statusPublished - May 1990

ASJC Scopus subject areas

  • Numerical Analysis
  • Modelling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

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