Quasiperiodicity involving twin oscillations in the complex Lorenz equations describing a detuned laser

Cun Zheng Ning, Hermann Haken

Research output: Contribution to journalArticle

15 Scopus citations

Abstract

Quasiperiodical motion in the complex Lorenz equations describing a detuned laser is shown to consist of twin oscillations: the first oscillation originates from Hopf bifurcation and the second is a parastic oscillation of the first one. Equations for the twin asymptotic oscillations are analytically derived in the center manifold, showing explicitly the parastic property of the second oscillation: its frequency is proportional to the square of the amplitude of the first one. The phase of the second oscillation shows also certain anholonomy which is very similar to the characteristics of Berry's phase. Numerical results show further that the first oscillation follows the sequence of bifurcations from simple periodic through period-doubling to chaos, as one continuously increases the control parameter, whereas the frequency of the parastic oscillation does not change qualitatively during the bifurcation process.

Original languageEnglish (US)
Pages (from-to)457-461
Number of pages5
JournalZeitschrift für Physik B Condensed Matter
Volume81
Issue number3
DOIs
StatePublished - Oct 1 1990
Externally publishedYes

ASJC Scopus subject areas

  • Condensed Matter Physics

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