Abstract

The equations describing the pulsating output of a laser containing a saturable absorber are investigated numerically and analytically. The laser admits a singular Hopf bifurcation to a nearly vertical branch of periodic solutions. Using asymptotic methods, we determine a simplified problem that describes the transition from harmonic to pulsating oscillations as the bifurcation parameter is changed. This transition occurs in a layer bounded by the Hopf bifurcation point, and by a critical point near which the branch of solutions becomes vertical.

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