Generalized Ginzburg-Landau equation for self-pulsing instability in a two-photon laser

Cun zheng Ning, Hermann Haken

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


A nonlinear analysis is made for a degenerate two-photon ring laser near its critical point corresponding to a self-pulsing instability by using the slaving principle and normal form theory. It turns out that the system undergoes two kinds of transitions, a usual Hopf bifurcation to a stable or unstable limit cycle and a co-dimension two Hopf bifurcation where the limit cycles disappear. An analytical criterion is given to distinguish the super-from the sub-critical bifurcation. We have also solved the equations numerically to confirm and to supplement our analytical results. In the case of super-critical bifurcation, a period-doubling bifurcation sequence to chaos is also observed with the decrease in pumping.

Original languageEnglish (US)
Pages (from-to)163-174
Number of pages12
JournalZeitschrift für Physik B Condensed Matter
Issue number1
StatePublished - Feb 1 1989
Externally publishedYes

ASJC Scopus subject areas

  • Condensed Matter Physics


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