On a codimension-four bifurcation occurring in optical bistability

  • G. Dangelmayr
  • M. Wegelin
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1463)


The subject of this paper is the unfolding of a singularity of vector fields in which a cusp and a degenerate Hopf bifurcation coalesce. This singularity has codimension four and appears in the mean field equations underlying optically bistable systems. We discuss the singularities of codimension smaller than four that occur as subsidiary bifurcations of the unfolding and present a two-dimensional section through the stability diagram.


Periodic Orbit Normal Form Hopf Bifurcation Phase Portrait Unstable Manifold 
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© Springer-Verlag 1991

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  • G. Dangelmayr
  • M. Wegelin

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