Singularity clustering in the Duffing oscillator

J. D. Fournier, G. Levine, Michael Tabor

Research output: Contribution to journalArticle

47 Citations (Scopus)

Abstract

An asymptotic and numerical study is made of the singularity structure, in the complex t-plane, of the Duffing oscillator. The presence of logarithmic terms in the local psi-series expansion, of the form t4 ln t, leads to a multisheeted singularity structure of great complexity. This structure is built recursively from an elemental pattern which takes the form of four-armed 'stars' of singularities. This construction is deduced analytically from the properties of the mapping z=t4 ln t and is confirmed quite accurately numerically. A systematic resummation of the psi series, in terms of Lame functions, is developed. This series exhibits the same analytic structure at all orders and provides a 'semi-local' analytical representation of the solution which is apparently valid even in the chaotic regime.

Original languageEnglish (US)
Article number014
Pages (from-to)33-54
Number of pages22
JournalJournal of Physics A: General Physics
Volume21
Issue number1
DOIs
StatePublished - 1988
Externally publishedYes

Fingerprint

Duffing Oscillator
Stars
oscillators
Clustering
Singularity
Lame functions
series expansion
Series
Series Expansion
Numerical Study
stars
Star
Logarithmic
Valid
Term
Form

ASJC Scopus subject areas

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

Cite this

Singularity clustering in the Duffing oscillator. / Fournier, J. D.; Levine, G.; Tabor, Michael.

In: Journal of Physics A: General Physics, Vol. 21, No. 1, 014, 1988, p. 33-54.

Research output: Contribution to journalArticle

Fournier, J. D. ; Levine, G. ; Tabor, Michael. / Singularity clustering in the Duffing oscillator. In: Journal of Physics A: General Physics. 1988 ; Vol. 21, No. 1. pp. 33-54.
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