2010, Rebrova, Natalia, Huyet, Guillaume, Rachinskii, Dmitrii, Vladimirov, Andrei G.

We study analytically and numerically a delay differential model of a passively mode-locked semiconductor laser subjected to a single frequency coherent injection. The width of the locking cone is calculated asymptotically in the limit of small injection and compared to that obtained by direct numerical integration of the model equations. The dependence of the locking cone on the laser parameters is discussed

2006, Schmid, Florian, Martins, J.A.C., Rebrova, Natalia

In this paper we announce some new mathematical results on the stability of quasi-static paths of a single particle linearly elastic system with Coulomb friction and persistent normal contact with a flat obstacle.A quasi-static path is said to be stable at some value of the load parameter if, for some finite interval of the load parameter thereafter, the dynamic solutions behave continuously with respect to the size of the initial perturbations (as in Lyapunov stability) and to the smallness of the rate of application of the external forces, $varepsilon$ (as in singular perturbation problems). In this paper we prove sufficient conditions for stability of quasi-static paths of a single particle linearly elastic system with Coulomb friction and persistent normal contact with a flat obstacle. The present system has the additional difficulty of its non-smoothness: the friction law is a multivalued operator and the dynamic evolutions of this system may have discontinuous accelerations.

2019, Vladimirov, Andrei G., Kovalev, Anton V., Viktorov, Evgeny A., Rebrova, Natalia, Huyet, Guillaume

Using a simple delay differential equation model we study theoretically the dynamics of a unidirectional class-A ring laser with a nonlinear amplifying loop mirror. We perform analytical linear stability analysis of the CW regimes in the large delay limit and demonstrate that these regimes can be destabilized via modulational and Turing-type instabilities, as well as by a bifurcation leading to the appearance of square-waves. We investigate the formation of square-waves and mode-locked pulses in the system. We show that mode-locked pulses are very asymmetric with exponential decay of the trailing and superexponential growth of the leading edge. We discuss asymmetric interaction of these pulses leading to a formation of harmonic mode-locked regimes.