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

Michael N. Vrahatis, Tassos Bountis, Nurit Budinsky

Research output: Contribution to journalArticle

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 - 1990
Externally publishedYes

Fingerprint

Bifurcation (mathematics)
Iterative methods
Orbits
orbits
Mathieu function
period doubling
Nonlinear equations
dynamical systems
newton
Dynamical systems
scaling
estimates

ASJC Scopus subject areas

  • Computer Science Applications
  • Physics and Astronomy(all)

Cite this

A convergence-improving iterative method for computing periodic orbits near Bifurcation Points. / Vrahatis, Michael N.; Bountis, Tassos; Budinsky, Nurit.

In: Journal of Computational Physics, Vol. 88, No. 1, 1990, p. 1-14.

Research output: Contribution to journalArticle

Vrahatis, Michael N. ; Bountis, Tassos ; Budinsky, Nurit. / A convergence-improving iterative method for computing periodic orbits near Bifurcation Points. In: Journal of Computational Physics. 1990 ; Vol. 88, No. 1. pp. 1-14.
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