Stability of equilibrium state in a laser with rapidly oscillating delay feedback

•We study stability of lasing under periodically modulated time delay feedback.•Minimum level of destabilizing FB versus amplitude modulation is found.•Control of stationary lasing fails in vicinity of subcritical bifurcation boundary.•We describe analytically limit cycle whose amplitude depends on modulation frequency.

Dynamics of laser with time-variable delayed feedback is analyzed in the neighborhood of the equilibrium. For the system, averaged over a rapidly variable, we obtain parameters at which the stationary state is stable. Stabilization of the stationary state due to modulation of the delay can be successful (unsuccessful) in domains adjacent to super (sub-) critical Hopf bifurcation boundaries. In a vicinity of the bifurcation points, stable and unstable periodic solutions are asymptotically described in dependence on the modulation frequency.