Filters

2015 - 201922020 - 20212

More filters

2019 - 201922020 - 20222
Reset filters

Settings

Type: Report × Subject: turbulence ×

Search Results

Now showing 1 - 4 of 4
  • Thumbnail Image
    Item
    Dynamical systems with multiple, long delayed feedbacks: Multiscale analysis and spatio-temporal equivalence
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Yanchuk, Serhiy; Giacomelli, Giovanni
    Dynamical systems with multiple, hierarchically long delayed feedback are introduced and studied. Focusing on the phenomenological model of a Stuart-Landau oscillator with two feedbacks, we show the multiscale properties of its dynamics and demonstrate them by means of a space-time representation. For sufficiently long delays, we derive a normal form describing the system close to the destabilization. The space and temporal variables, which are involved in the space-time representation, correspond to suitable timescales of the original system. The physical meaning of the results, together with the interpretation of the description at different scales, is presented and discussed. In particular, it is shown how this representation uncovers hidden multiscale patterns such as spirals or spatiotemporal chaos. The effect of the delays size and the features of the transition between small to large delays is also analyzed. Finally, we comment on the application of the method and on its extension to an arbitrary, but finite, number of delayed feedback terms.
  • Thumbnail Image
    Item
    Nonlinear dynamical properties of frequency swept fiber-based semiconductor lasers
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2021) Slepneva, Svetlana; Pimenov, Alexander
    We investigate dynamics of semiconductor lasers with fiber-based unidirectional ring cavity that can be used as frequency swept sources. We identify key factors behind the reach dynamical behaviour of such lasers using state-of-the-art experimental and analytical methods. Experimentally, we study the laser in static, quasi-static and synchronisation regimes.We apply experimental methods such as optical heterodyne or electric field reconstruction in order to characterise these regimes or study the mechanisms of transition between them. Using a delay differential equation model, we demonstrate that the presence of chromatic dispersion can lead to destabilisation of the laser modes through modulational instability, which results in undesirable chaotic emission. We characterise the instability threshold both theoretically and experimentally, and demonstrate deterioration of the FDML regime near the threshold.
  • Thumbnail Image
    Item
    Turbulent coherent structures in a long cavity semiconductor laser near the lasing threshold
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2020) Gowda, Uday; Roche, Amy; Pimenov, Alexander; Vladimirov, Andrei G.; Slepneva, Svetlana; Viktorov, Evgeny A.; Huyet, Guillaume
    We report on the formation of novel turbulent coherent structures in a long cavity semiconductor laser near the lasing threshold. Experimentally, the laser emits a series of power dropouts within a roundtrip and the number of dropouts per series depends on a set of parameters including the bias current. At fixed parameters, the drops remain dynamically stable, repeating over many roundtrips. By reconstructing the laser electric field in the case where the laser emits one dropout per round trip and simulating its dynamics using a time-delayed model, we discuss the reasons for long-term sustainability of these solutions. We suggest that the observed dropouts are closely related to the coherent structures of the cubic complex Ginzburg-Landau equation.
  • Thumbnail Image
    Item
    Turbulence in the Ott-Antonsen equation for arrays of coupled phase oscillators
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Wolfrum, Matthias; Gurevich, Svetlana V.; Omelchenko, Oleh E.
    In this paper we study the transition to synchrony in an one-dimensional array of oscillators with non-local coupling. For its description in the continuum limit of a large number of phase oscillators, we use a corresponding Ott-Antonsen equation, which is an integrodifferential equation for the evolution of the macroscopic profiles of the local mean field. Recently, it has been reported that in the spatially extended case at the synchronization threshold there appear partially coherent plane waves with different wave numbers, which are organized in the well-known Eckhaus scenario. In this paper, we show that for Kuramoto-Sakaguchi phase oscillators the phase lag parameter in the interaction function can induce a Benjamin-Feir type instability of the partially coherent plane waves. The emerging collective macroscopic chaos appears as an intermediate stage between complete incoherence and stable partially coherent plane waves.We give an analytic treatment of the Benjamin-Feir instability and its onset in a codimension-two bifurcation in the Ott-Antonsen equation as well as a numerical study of the transition from phase turbulence to amplitude turbulence inside the Benjamin-Feir unstable region.