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- ItemRobust homoclinic orbits in planar systems with Preisach hysteresis operator(Bristol : IOP Publ., 2016) Pimenov, Alexander; Rachinskii, DmitriiWe construct examples of robust homoclinic orbits for systems of ordinary differential equations coupled with the Preisach hysteresis operator. Existence of such orbits is demonstrated for the first time. We discuss a generic mechanism that creates robust homoclinic orbits and a method for finding them. An example of a homoclinic orbit in a population dynamics model with hysteretic response of the prey to variations of the predator is studied numerically.
- ItemBistability and hysteresis in an optically injected two-section semiconductor laser(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Pimenov, Alexander; Viktorov, Evgeniy A.; Hegarty, Stephen P.; Habruseva, Tatiana; Huyet, Guillaume; Rachinskii, Dmitrii; Vladimirov, Andrei G.The effect of coherent single frequency injection on two-section semiconductor lasers is studied numerically using a model based on a set of delay differential equations. The existence of bistability between different CW and non-stationary regimes of operation is demonstrated in the case of sufficiently large linewidth enhancement factors.
- ItemHomoclinic orbits in a two-patch predator-prey model with Preisach hysteresis operator(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Pimenov, Alexander; Rachinskii, DmitriiSystems of operator-differential equations which hysteresis operators can have unstable equilibrium points with an open basin of attraction. In this paper, a numerical example of a robust homoclinic loop is presented for the first time in a population dynamics model with hysteretic response of prey to variations of predator. A mechanism creating this homoclinic trajectory is discussed.
- ItemTiming jitter of passively mode-locked semiconductor lasers subject to optical feedback : a semi-analytic approach(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Jaurigue, Lina; Pimenov, Alexander; Rachinskii, Dmitrii; Schöll, Eckehard; Lüdge, Kathy; Vladimirov, Andrei G.We propose a semi-analytical method of calculating the timing fluctuations in modelocked semiconductor lasers and apply it to study the effect of delayed coherent optical feedback on pulse timing jitter in these lasers. The proposed method greatly reduces computation times and therefore allows for the investigation of the dependence of timing fluctuations over greater parameter domains. We show that resonant feedback leads to a reduction in the timing jitter and that a frequency-pulling region forms about the main resonances, within which a timing jitter reduction is observed. The width of these requency pulling regions increases linearly with short feedback delay times. We derive an analytic expression for the timing jitter, which predicts a monotonic decrease in the timing jitter for resonant feedback of increasing delay lengths, when timing jitter effects are fully separated from amplitude jitter effects. For long feedback cavities the decrease in timing jitter scales approximately as 1/tau with the increase of the feedback delay time tau.
- ItemTiming jitter in passively mode-locked semiconductor lasers(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Pimenov, Alexander; Rachinskii, Dmitrii; Habruseva, Tatiana; Hegarty, Stephen P.; Guillaume, Huyet; Vladimirov, Andrei G.We study the effect of noise on the dynamics of passively mode-locked semiconductor lasers both experimentally and theoretically. A method combining analytical and numerical approaches for estimation of pulse timing jitter is proposed. We investigate how the presence of dynamical features such as wavelength bistability affects timing jitter.
- ItemRobust homoclinic orbits in planar systems with Preisach hysteresis operator(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Pimenov, Alexander; Rachinskii, DmitriiWe construct examples of robust homoclinic orbits for systems of ordinary differential equations coupled with the Preisach hysteresis operator. Existence of such orbits is demonstrated for the first time. We discuss a generic mechanism that creates robust homoclinic orbits and a method for finding them. An example of a homoclinic orbit in a population dynamics model with hysteretic response of the prey to variations of the predator is studied numerically.
- ItemStability results for a soil model with singular hysteretic hydrology(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Krejčí, Pavel; O'Kane, J. Philip; Pokrovskii, Alexei; Rachinskii, DmitriiWe consider a differential equation describing the mass balance in a soil hydrology model with noninvertible Preisach-type hysteresis. We approximate the singular Preisach operator by regular ones and show, as main result, that the solutions of the regularized problem converge to a solution of the original one as the regularization parameter tends to zero. For monotone right hand sides, we prove that the solution is unique. If in addition the external water sources are time periodic, then we find sufficient conditions for the existence, uniqueness, and asymptotic stability of periodic solutions.
- ItemBifurcations in a model of monolithic passively mode-locked semiconductior laser(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Vladimirov, Andrei; Pimenov, Alexander; Rachinskii, DmitriiBifurcation mechanisms of the development and break up of different operation regimes in a passively mode-locked monolithic semiconductor laser are studied by solving numerically partial differential equations for amplitudes of two counterpropagating waves and carrier densities in gain and absorber sections. It is shown that harmonic mode-locking regime with two pulses in the cavity can exhibit a period-doubling bifurcation leading to different amplitudes and separations of the pulses. The effect of linewidth enhancement factors in gain and absorber sections on the laser dynamics is discussed.
- ItemAn optically injected mode locked laser(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 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
- ItemDynamical regimes in a monolithic passively mode-locked quantum dot laser(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Vladimirov, Andrei; Bandelow, Uwe; Fiol, Gerrit; Arsenijevi´c, Dejan; Kleinert, Moritz; Bimberg, Dieter; Pimenov, Alexander; Rachinskii, DmitriiOperation regimes of a two section monolithic quantum dot (QD) mode-locked laser are studied experimentally and theoretically, using a model that takes into account carrier exchange between QD ground state and 2D reservoir of a QD-in-a-well structure, and experimentally. It is shown analytically and numerically that, when the absorber section is long enough, the laser exhibits bistability between laser off state and different mode-locking regimes. The Q-switching instability leading to slow modulation of the mode-locked pulse peak intensity is completely eliminated in this case. When, on the contrary, the absorber length is rather short, in addition to usual Q-switched mode-locking, pure Q-switching regimes are predicted theoretically and observed experimentally.