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On a codimension-four bifurcation occurring in optical bistability

Part of the Lecture Notes in Mathematics book series (LNM,volume 1463)

Abstract

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.

Keywords

  • Periodic Orbit
  • Normal Form
  • Hopf Bifurcation
  • Phase Portrait
  • Unstable Manifold

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 1991 Springer-Verlag

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Dangelmayr, G., Wegelin, M. (1991). On a codimension-four bifurcation occurring in optical bistability. In: Roberts, M., Stewart, I. (eds) Singularity Theory and its Applications. Lecture Notes in Mathematics, vol 1463. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0085428

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  • DOI: https://doi.org/10.1007/BFb0085428

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  • Print ISBN: 978-3-540-53736-6

  • Online ISBN: 978-3-540-47047-2

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