Biomedical subjects
Publications and source records attributed to A G Vladimirov.
We study the stability of localized structures in a passive optical bistable system. We show that there is a critical value of the input field intensity above which localized structures are unstable with respect to a curvature instability. Beyond this instability boundary, a transition from the localized branch of solutions to stable hexagons is found.
We study the dynamics of an array of single mode semiconductor lasers globally but weakly coupled by a common external feedback mirror and by nearest neighbor interactions. We seek to determine the conditions under which all lasers of the array are in phase, whether in a steady, periodic, quasiperiodic, or chaotic regime, in order to maximize the output far field intensity. We show that the delay may be a useful control parameter to achieve in-phase synchronization. For the in-phase steady state, there is a competition between a delay-induced Hopf bifurcation leading to an in-phase periodic regime and a delay-independent Hopf bifurcation leading to an antiphased periodic regime. Both regimes are described analytically and secondary Hopf bifurcations to quasiperiodic solutions are found. Close to the stable steady state, the array is described by a set of Kuramoto equations for the phases of the fields. Above the first Hopf bifurcation, these equations are generalized by the addition of second and third order time derivatives of the phases.
Differential equations describing the interaction of two weakly overlapping autosolitons in the transverse section of a wide-aperture laser with a saturable absorber are derived and analyzed. The existence of in-phase and out-of-phase stable bound autosoliton states is predicted analytically and confirmed numerically.
We study analytically the (N-1)-fold degenerate Hopf bifurcation at which N stationary modes with identical parameters become unstable in a model of a solid-state laser with intracavity second harmonic generation. We use the normal form method and exploit the symmetries of the problem. Up to N=3, stable periodic antiphased solutions emerge from the Hopf bifurcation. For N=4, stable quasiperiodic solutions arise from the degenerate Hopf bifurcation. For N>4, the quasiperiodic solutions may be unstable. Then chaotic itineracy is observed numerically close to the degenerate Hopf bifurcation.