Determining an Organizing Center for Passive Optical Systems
The Maxwell-Bloch equations underlying passive optical systems are considered. Using MAPLE we determine a highly degenerate singularity which corresponds to the coalescence of a cusp and a degenerate Hopf bifurcation with broken transversality condition. The dynamics associated with the unfolding of this singularity gives rise to a rich variety of different behaviour including, for example, two types of infinite period bifurcations on tori.
KeywordsPeriodic Orbit Hopf Bifurcation Phase Portrait Bifurcation Diagram Center Manifold
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- G. Dangelmayr, M. Wegelin, On a codimension four bifurcation ocurring in optical bistability, in: Proceedings of the Workshop on Dynamics, Bifurcations and Singularity Theory, 10–14 July 1989, Warwick, to appear.Google Scholar
- M. Golubitsky, D. Schaeffer: Singularities and Groups in Bifurcation Theory, Vol.I, Springer 1985.Google Scholar
- J. Guckenheimer, P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer 1983.Google Scholar
- L. A. Lugiato, V. Benza, L. M. Narducci, Optical bistability, self-pulsing and higher-order bifurcations, in H. Haken (ed.): Evolution of Order and Chaos in Physics, Chemistry, and Biology, Springer 1982.Google Scholar
- L. A. Lugiato, L. M. Narducci, R. Lefever, Instabilities, spatial and temporal patterns in passive optical systems, in R. Graham, A. Wunderlin (eds.): Lasers and Synergetics. A Colloquium on Coherence and Self-Organization in Nature, Springer 1987.Google Scholar