Abstract
We study the dynamics of a laser with saturable absorber near the bifurcation point where the stationary solution encounters bifurcation with fourfold zero eigenvalue. This degeneracy results from a symmetry typical to laser systems with exact resonance and the bifurcation problem may be considered as an extension of the well-known bifurcation with doubly zero eigenvalue to systems in complex variables or as an example of bifurcation with two parameters in three-dimensional real system. We investigate phase portraits of such system and display corresponding bifurcation diagrams for a laser model.
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