Explicit centre manifold reduction and full bifurcation analysis for an astigmatic Maxwell - Bloch laser
نویسندگان
چکیده
We set up a general framework to study the bifurcations of nearly degenerate modes of a Maxwell-Bloch laser model, and we apply it specifically to the study of interactions of two modes of a laser with broken circular symmetry. We use an explicit centre manifold reduction to analyse the behaviour of this laser. Complex bifur-cation sequences involving single mode solutions, mode locking and mode beating regimes are predicted. These sequences are organized by a Hopf bifurcation with 1 : 1 resonance and a Z 2-symmetric Takens-Bogdanov bifurcation. Numerical simulations of the original system show good agreement with theory.
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