Structurally stable phase portraits for the five-dimensional Lorenz equations

G. Dangelmayr, M. Neveling, D. Armbruster

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


We discuss the universal unfolding of a planar codimension four singularity which occurs in the five dimensional Lorenz equations. All structurally stable phase portraits are given and some representative bifurcation diagrams are displayed. These phase portraits have a rich structure including up to four limit cycles. The bifurcation sets in unfolding space - where the phase portraits undergo a qualitative change - are determined and new types of saddle loops are found. We show that the codimension four singularity occurs stably in a model for the laser with saturable absorber. Solution branches indicating birhythmicity and saddle loops for the pulsed mode of laser operation are found in bifurcation diagrams corresponding to the universal unfolding of the codimension four singularity. This explains numerical solutions of other authors which so far have not been related to a bifurcation analysis. Hints to other Lorenz models are given.

Original languageEnglish (US)
Pages (from-to)491-501
Number of pages11
JournalZeitschrift für Physik B Condensed Matter
Issue number4
StatePublished - Dec 1 1986
Externally publishedYes

ASJC Scopus subject areas

  • Condensed Matter Physics


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