Belarus State Economic University, Belarus

In recent years, the efficiency of dynamic control by using a variable delayed feedback (FB) is actively discussed. Schemes with high-frequency modulation of the delay time and of the diving amplitude have been considered, see, for example, Phys.Rev. E 88, 032912 (2013), Physica D, 2014. However, such high-frequency modulation may be rather difficult to implement in class B lasers. In this paper we study the local dynamics of a laser with incoherent optical delayed feedback, whose parameters are modulated in resonant way, i.e. modulated with a frequency comparable with characteristic ones. We derive the normal forms describing the dynamics in a vicinity of stability boundary of the equilibrium. They indicate alternation of super- and subcritical Hopf bifurcations along the boundary. On the base of normal forms we determine parameters of FB line and modulation amplitude and frequency in order to stabilize stationary generation.