Publications
Articles in Refereed Journals

F. Severing, U. Bandelow, S. Amiranashvili, Spurious fourwave mixing processes in generalized nonlinear Schrödinger equations, Journal of Lightwave Technology, (2023), pp. 16, DOI 10.1109/JLT.2023.3261804 .
Abstract
Numerical solutions of a nonlinear Schödinger equation, e.g., for pulses in optical fibers, may suffer from the spurious fourwave mixing processes. We study how these nonphysical resonances appear in solutions of a much more stiff generalized nonlinear Schödinger equation with an arbitrary dispersion operator and determine the necessary restrictions on temporal and spatial resolution of a numerical scheme. The restrictions are especially important to meet when an envelope equation is applied in a wide spectral window, e.g., to describe supercontinuum generation, in which case the appearance of the numerical instabilities can occur unnoticed. 
M. Stöhr, M. Wolfrum, Temporal dissipative solitons in the MorrisLecar model with timedelayed feedback, Chaos. An Interdisciplinary Journal of Nonlinear Science, 33 (2023), pp. 023117/1023117/9, DOI 10.1063/5.0134815 .
Abstract
We study the dynamics and bifurcations of temporal dissipative solitons in an excitable system under timedelayed feedback. As a prototypical model displaying different types of excitability we use the MorrisLecar model. In the limit of large delay soliton like solutions of delaydifferential equations can be treated as homoclinic solutions of an equation with an advanced argument. Based on this, we use concepts of classical homoclinic bifurcation theory to study different types of pulse solutions and to explain their dependence on the system parameters. In particular, we show, how a homoclinic orbit flip of a single pulse soliton leads to the destabilization of equidistant multipulse solutions and to the emergence of stable pulse packages. It turns out that this transition is induced by a heteroclinic orbit flip in the system without feedback, which is related to the excitability properties of the MorrisLecar model 
A. Pimenov, A.G. Vladimirov, Temporal solitons in an optically injected Kerr cavity with two spectral filters, Optics, 3(4) (2022), pp. 364383, DOI 10.3390/opt3040032 .
Abstract
We investigate theoretically the dynamical behavior of an optically injected Kerr cavity where the chromatic dispersion is induced by propagation of light through two Lorentzian spectral filters with different widths and central frequencies. We show that this setup can be modeled by a second order delay differential equation that can be considered as a generalization of the Ikeda map with included spectral filtering, dispersion, and coherent injection terms. We demonstrate that this equation can exhibit modulational instability and bright localized structures formation in the anomalous dispersion regime. 
A. Hajizadeh, A. Matysiak, M. Wolfrum, P.J.C. May, R. König, Auditory cortex modelled as a dynamical network of oscillators: Understanding eventrelated fields and their adaptation, Biological Cybernetics, 116 (2022), pp. 475499, DOI 10.1007/s00422022009367 .
Abstract
Adaptation, the reduction of neuronal responses by repetitive stimulation, is a ubiquitous feature of auditory cortex (AC). It is not clear what causes adaptation, but shortterm synaptic depression (STSD) is a potential candidate for the underlying mechanism. We examined this hypothesis via a computational model based on AC anatomy, which includes serially connected core, belt, and parabelt areas. The model replicates the eventrelated field (ERF) of the magnetoencephalogram as well as ERF adaptation. The model dynamics are described by excitatory and inhibitory state variables of cell populations, with the excitatory connections modulated by STSD. We analysed the system dynamics by linearizing the firing rates and solving the STSD equation using timescale separation. This allows for characterization of AC dynamics as a superposition of damped harmonic oscillators, socalled normal modes. We show that repetition suppression of the N1m is due to a mixture of causes, with stimulus repetition modifying both the amplitudes and the frequencies of the normal modes. In this view, adaptation results from a complete reorganization of AC dynamics rather than a reduction of activity in discrete sources. Further, both the network structure and the balance between excitation and inhibition contribute significantly to the rate with which AC recovers from adaptation. This lifetime of adaptation is longer in the belt and parabelt than in the core area, despite the time constants of STSD being spatially constant. Finally, we critically evaluate the use of a single exponential function to describe recovery from adaptation. 
A.A. Grin, K.R. Schneider, Global algebraic PoincaréBendixson annulus for the van der Pol systems, Differential Equations, 58 (2022), pp. 285295, DOI 10.1134/S0012266122030016 .
Abstract
By means of planar polynomial systems topologically equivalent to the van der Pol system we demonstrate an approach to construct algebraic transversal ovals forming a parameter depending PoincaréBendixson annulus which contains a unique limit cycle for the full parameter domain. The inner boundary consists of the zerolevel set of a special DulacCherkas function which implies the uniqueness of the limit cycle. For the construction of the outer boundary we present a corresponding procedure 
L. Schülen, A. Gerdes, M. Wolfrum, A. Zakharova, Solitary routes to chimera state, Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, 106 (2022), pp. L042203/1L042203/5, DOI 10.1103/PhysRevE.106.L042203 .
Abstract
We show how solitary states in a system of globally coupled FitzHughNagumo oscillators can lead to the emergence of chimera states. By a numerical bifurcation analysis of a suitable reduced system in the thermodynamic limit we demonstrate how solitary states, after emerging from the synchronous state, become chaotic in a perioddoubling cascade. Subsequently, states with a single chaotic oscillator give rise to states with an increasing number of incoherent chaotic oscillators. In large systems, these chimera states show extensive chaos. We demonstrate the coexistence of many of such chaotic attractors with different Lyapunov dimensions, due to different numbers of incoherent oscillators. 
S. Yanchuk, M. Wolfrum, T. Pereira, D. Turaev, Absolute stability and absolute hyperbolicity in systems with discrete timedelays, Journal of Differential Equations, 318 (2022), pp. 323343, DOI 10.1016/j.jde.2022.02.026 .
Abstract
An equilibrium of a delay differential equation (DDE) is absolutely stable, if it is locally asymptotically stable for all delays. We present criteria for absolute stability of DDEs with discrete timedelays. In the case of a single delay, the absolute stability is shown to be equivalent to asymptotic stability for sufficiently large delays. Similarly, for multiple delays, the absolute stability is equivalent to asymptotic stability for hierarchically large delays. Additionally, we give necessary and sufficient conditions for a linear DDE to be hyperbolic for all delays. The latter conditions are crucial for determining whether a system can have stabilizing or destabilizing bifurcations by varying time delays. 
S. Amiranashvili, U. Bandelow, Unusual scenarios in fourwavemixing instability, Physical Review A, 105 (2022), pp. 063519/1063519/6, DOI 10.1103/PhysRevA.105.063519 .
Abstract
A pump carrier wave in a dispersive system may decay by giving birth to blue and redshifted satellite waves due to modulation or fourwave mixing instability. We analyse situations where the satellites are so different from the carrier wave, that the redshifted satellite either changes its propagation direction (k < 0, ω > 0) or even gets a negative frequency (k, ω < 0). Both situations are beyond the envelope approach and require application of Maxwell equations. 
M. Radziunas, Calculation of steady states in dynamical semiconductor laser models, Optical and Quantum Electronics, 55 (2023), pp. 121/1121/14 (published online on 17.12.2022), DOI 10.1007/s11082022043851 .
Abstract
We discuss numerical challenges in calculating stable and unstable steady states of widely used dynamical semiconductor laser models. Knowledge of these states is valuable when analyzing laser dynamics and different properties of the lasing states. The example simulations and analysis mainly rely on 1(time)+1(space)dimensional travelingwave models, where the steady state defining conditions are formulated as a system of nonlinear algebraic equations. The per formed steady state calculations reveal limitations of the LangKobayashi model, explain nontrivial bias threshold relations in lasers with several electrical contacts, or predict and explain transient dynamics when simulating such lasers. 
A.G. Vladimirov, Short and longrange temporal cavity soliton interaction in delay models of modelocked lasers, Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, 105 (2022), pp. 044207/1044207/6, DOI 10.1103/PhysRevE.105.044207 .
Abstract
Interaction equations governing slow time evolution of the coordinates and phases of two interacting temporal cavity solitons in a delay differential equation model of a nonlinear mirror modelocked laser are derived and analyzed. It is shown that nonlocal pulse interaction due to gain depletion and recovery can lead either to a development of harmonic modelocking regime, or to a formation of closely packed incoherent soliton bound state with weakly oscillating intersoliton time separation. Local interaction via electric field tails can result in an antiphase or inphase stationary or breathing harmonic modelocking regime. 
M. Wolfrum, S. Yanchuk, O. D'huys, Multiple selflocking in the KuramotoSakaguchi system with delay, SIAM Journal on Applied Dynamical Systems, 21 (2022), pp. 17091725, DOI 10.1137/21M1458971 .
Abstract
We study the KuramotoSakaguchi system of phase oscillators with a delayed meanfield coupling. By applying the theory of large delay to the corresponding OttAntonsen equation, we explain fully analytically the mechanisms for the appearance of multiple coexisting partially locked states. Closely above the onset of synchronization, these states emerge in the Eckhaus scenario: with increasing coupling, more and more partially locked states appear unstable from the incoherent state, and gain stability for larger coupling at a modulational stability boundary. The partially locked states with strongly detuned frequencies are shown to emerge subcritical and gain stability only after a fold and a series of Hopf bifurcations. We also discuss the role of the Sakaguchi phase lag parameter. For small delays, it determines, together with the delay time, the attraction or repulsion to the central frequency, which leads to supercritical or subcritical behavior, respectively. For large delay, the Sakaguchi parameter does not influence the global dynamical scenario.
Contributions to Collected Editions

A.V. Kovalev, K.M. Grigorenko, S. Slepneva, N. Rebrova, A.G. Vladimirov, G. Huyet, E.A. Viktorov, Bifurcation bridges In modelocked frequencyswept feedback lasers, in: 2022 International Conference Laser Optics (ICLO), Saint Petersburg, Russian Federation, 2022, IEEE, 2022, pp. 11, DOI 10.1109/ICLO54117.2022.9839784 .
Abstract
We describe and explain the periodic modelocked regime and its mechanisms of occurrence in a frequency swept SGDBR laser source with continuous optical feedback. We propose that modelocked operation results from the resonant perturbation of bridges of periodic solutions existing in a nonswept system with feedback. 
M. Kantner, L. Mertenskötter, DataDriven modeling of NonMarkovian noise in semiconductor lasers, in: 22nd International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD), J. Piprek, P. Bardella, eds., IEEE Xplorer, 2022, pp. 5758, DOI 10.1109/NUSOD54938.2022.9894788 .
Abstract
NonMarkovian noise degrades the coherence properties of semiconductor lasers and contributes significantly to broadening of the linewidth. Since modeling of such colored noise systems from first principles is not accessible, we aim for a datadriven modeling approach in which a system of stochastic rate equations shall be reconstructed from time series data. 
M. Radziunas, Steady states in dynamical semiconductor laser models and their analysis, in: 2022 International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD), Turin, Italy, 2022, J. Piprek, P. Bardella, eds., IEEE, 2022, pp. 4950, DOI 10.1109/NUSOD54938.2022.9894775 .
Abstract
We present an algorithm for calculating steady states in the dynamic PDE model for SLs admitting gain compression, spatial hole burning, and multilevel carrier rate equations. Presented example simulations rely on 1(time)+1(space)dimensional travelingwave and LangKobayashitype models.
Preprints, Reports, Technical Reports

A.G. Vladimirov, Temporal cavity soliton interaction in passively modelocked semiconductor lasers, Preprint no. 3001, WIAS, Berlin, 2023, DOI 10.20347/WIAS.PREPRINT.3001 .
Abstract, PDF (525 kByte)
Weak interaction due to gain saturation and recovery of temporal cavity solitons in a delay differential model of a long cavity semiconductor laser is studied numerically and analytically using an asymptotic approach. It is shown that apart from usual soliton repulsion leading to a harmonic modelocking regime a soliton attraction is also possible in a laser with nonzero linewidth enhancement factor. It is shown numerically that the attraction can lead either to a soliton merging or to a pulse bound state formation. 
A. Roche, S. Slepneva, A. Kovalev, A. Pimenov, A.G. Vladimirov, M. Marconi, M. Giudici, G. Huyet, Decoherence and turbulence sources in a long laser, Preprint no. 2988, WIAS, Berlin, 2022, DOI 10.20347/WIAS.PREPRINT.2988 .
Abstract, PDF (3636 kByte)
We investigate the turnon process in a laser cavity where the roundtrip time is several orders of magnitude greater than the active medium timescales. In this long delay limit the electromagnetic field buildup can be mapped experimentally roundtrip after roundtrip. We show how coherence settles down starting from a stochastic initial condition. In the early stages of the turnon, we show that power dropouts emerge, persist for several roundtrips and seed dark solitons. These latter structures exhibit a chaotic dynamics and emit radiation that can lead to an overall turbulent dynamics depending on the cavity dispersion. 
M. Kantner, L. Mertenskötter, Improved laser linewidth estimation from selfheterodyne beat note measurements using parametric Wiener filters, Preprint no. 2983, WIAS, Berlin, 2022, DOI 10.20347/WIAS.PREPRINT.2983 .
Abstract, PDF (3037 kByte)
Selfheterodyne beat note measurement techniques are widely used for the experimental char acterization of the phase noise power spectral density (PSD) and the spectral linewidth of lasers. The measured data, however, must be corrected for the transfer function of the interferometer in a postprocessing routine. The standard approach disregards the measurement noise and thereby induces uncontrolled artifacts in the reconstructed noise PSDs. We introduce an improved data postprocessing routine based on a parametric Wiener filter (power spectrum equalization, PSE), that is potentially free of reconstruction artifacts provided a good estimate for the signaltonoise ratio (SNR) is supplied. Based on the PSE filter, we describe a new method for the estimation of the intrinsic laser linewidth. Our method yields accurate estimates even in the case of strong measurement noise, where the intrinsic linewidth plateau is not visible using the standard method. We demonstrate the method using simulated data from a stochastic laser rate equation model. 
F. Severing, U. Bandelow, S. Amiranashvili, Spurious fourwave mixing processes in generalized nonlinear Schrödinger equations, Preprint no. 2975, WIAS, Berlin, 2022.
Abstract, PDF (3907 kByte)
Numerical solutions of a nonlinear Schödinger equation, e.g., for pulses in optical fibers, may suffer from the spurious fourwave mixing processes. We study how these nonphysical resonances appear in solutions of a much more stiff generalized nonlinear Schödinger equation with an arbitrary dispersion operator and determine the necessary restrictions on temporal and spatial resolution of a numerical scheme. The restrictions are especially important to meet when an envelope equation is applied in a wide spectral window, e.g., to describe supercontinuum generation, in which case the appearance of the numerical instabilities can occur unnoticed. 
A. Pimenov, A.G. Vladimirov, Temporal solitons in an optically injected Kerr cavity with two spectral filters, Preprint no. 2948, WIAS, Berlin, 2022, DOI 10.20347/WIAS.PREPRINT.2948 .
Abstract, PDF (990 kByte)
We investigate theoretically the dynamical behavior of an optically injected Kerr cavity where the chromatic dispersion is induced by propagation of light through two Lorentzian spectral filters with different widths and central frequencies. We show that this setup can be modeled by a second order delay differential equation that can be considered as a generalization of the Ikeda map with included spectral filtering, dispersion, and coherent injection terms. We demonstrate that this equation can exhibit modulational instability and bright localized structures formation in the anomalous dispersion regime. 
S. Amiranashvili, Modeling of ultrashort optical pulses in nonlinear fibers, Preprint no. 2918, WIAS, Berlin, 2022, DOI 10.20347/WIAS.PREPRINT.2918 .
Abstract, PDF (17 MByte)
This work deals with theoretical aspects of pulse propagation. The core focus is on extreme, fewcycle pulses in optical fibers, pulses that are strongly affected by both dispersion and nonlinearity. Using Hamil tonian methods, we discuss how the meaning of pulse envelope changes, as pulses become shorter and shorter, and why an envelope equation can still be used. We also discuss how the standard set of dispersion coefficients yields useful rational approximations for the chromatic dispersion in optical fibers. Three more specific problems are addressed thereafter. First, we present an alternative framework for ultra short pulses in which nonenvelope propagation models are used. The approach yields the limiting, shortest solitons and reveals their universal features. Second, we describe how one can manipulate an ultrashort pulse, i.e., to change its amplitude and duration in a predictable manner. Quantitative theory of the manipu lation is presented based on perturbation theory for solitons and analogy between classical fiber optics and quantum mechanics. Last but not least, we consider a recently found alternative to the standard splitstep approach for numerical solutions of the pulse propagation equations.
Talks, Poster

L. Mertenskötter, Kalman filtering of stochastic laser dynamics: Parameter and state space estimation from timedelayed measurements, International Conference on Structural Nonlinear International Conference on Structural Nonlinea, May 15  17, 2023, Marrakech, Morocco.

S. Amiranashvili, Numerical aspects of modulation instability, 26th International Conference on Mathematical Modelling and Analysis, University of Latvia, Riga, Lithuania, June 1, 2023.

S. Amiranashvili, Numerical aspects of modulation instability, 26th International Conference on Mathematical Modelling and Analysis, University of Latvia, Riga, Lithuania, June 1, 2023.

U. Bandelow, Modeling and simulation of seminconductor devices: From highpower lasers to quantum technologies, Winter School on IIISB Applications: NonVolatile memories A modelling perspective, Technische Universität Berlin, February 27, 2023.

M. Radziunas, Modeling of photonic crystal surfaceemitting lasers, 26th International Conference on Mathematical Modelling and Analysis, University of Latvia, Riga, Lithuania, May 30, 2023.

M. Radziunas, Modeling, simulation, and analysis of dynamics in semiconductor lasers: A brief overview of the WIASFBH collaboration, Leibniz MMS Days 2023, LeibnizInstitut für Agrartechnik und Bioökonomie, Potsdam.

M. Wolfrum, Phase sensitive excitability of a limit cycle, Conference on Nonlinear Data Analysis and Modeling: Advances, Appilcations, Perspective, March 15  17, 2023.

A. Pimenov, Localized structures in a passive ring cavity with two filters under optical injection, Nonlinear Waves and Turbulence in Photonics 2022, WIAS Berlin, July 15, 2022.

M. Stöhr, Bifurcations and instabilities of temporal dissipative solions in DDEsystems with large delay, Workshop on Control of SelfOrganizing Nonlinear Systems, September 26  28, 2022.

M. Stöhr, Bifurcations and instabilities of temporal dissipative solions in DDEsystems with large delay, DMV Annual Meeting 2022, September 16  22, 2022, Freie Universität Berlin, September 16, 2022.

M. Stöhr, Bifurcations and instabilities of temporal dissipative solitons in DDEsystems with large delay, International Conference on Control of Self Organizing Nonlinear Systems, Potsdam, November 23  26, 2022.

A. Gerdes, Synchronization patterns in globally coupled StuartLandau oscillators, FrenchGerman WEHeraeusSeminar : Outstanding Challenges in Nonlinear Dynamics, Les Houches, France, March 20  25, 2022.

A. Gerdes, Synchronization patterns in globally coupled StuartLandau oscillators, Leibniz MMS Days 2022, Potsdam, April 25  27, 2022.

A. Gerdes, Synchronization patterns in globally coupled StuartLandau oscillators, Dynamics Days Europe 2022, Aberdeen, UK, August 22  26, 2022.

A. Gerdes, Synchronization patterns in globally coupled StuartLandau oscillators, Workshop on Control of SelfOrganizing Nonlinear Systems, September 26  28, 2022, LEUCOREA Tagungszentrum, Lutherstadt Wittenberg, September 27, 2022.

L. Mertenskötter, M. Kantner, U. Bandelow, H. Wenzel, NonMarkovian noise in semiconductor lasers, MATH+ Day 2022, Berlin, November 18, 2022.

L. Mertenskötter, DataDriven modeling of NonMarkovian noise in semiconductor laser, 22nd International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD), September 12  16, 2022, Politecnico di Torino, Italy.

A. Pimenov, Chromatic dispersion in delayed differential equations for optical cavities and localized structures, MURPHYS 2022 International Conference on Multiple Scale Systems and Hysteresis, May 30  June 3, 2022, Mathematical Institute, Silesian University, Opava, Czech Republic, May 30, 2022.

S. Amiranashvili, Unusual ways of fourwave mixing instability, Nonlinear Waves and Turbulence in Photonics 2022, WIAS Berlin, July 14, 2022.

F. Severing, How numerics add to the instabilities of the generalised nonlinear Schrödinger equation, Nonlinear Waves and Turbulence in Photonics 2022, Berlin, July 14  15, 2022.

F. Severing , Nonlinear Schrödinger Equation  Flawless description of modulation instability?, Student Chapter Poster Session (SCPS) 2022 (Online Event), Sussex, UK, February 20, 2022.

F. Severing , How numerics add to the instabilities of the generalised nonlinear Schrödinger equation, Minisymposium for Young Researchers 2022, WIAS Berlin, July 21, 2022.

S. Amiranashvili, Seminar zum Thema: Nicht Hermiteschen Operationen, August 10  11, 2022, TU Wien, Austria.

M. Radziunas, Modeling and simulation of semiconductor lasers for high emission power applications, 25th International Conference Mathematical Modelling and Analysis, May 30  June 2, 2022, Vilnius Gediminas Technical University, Druskininkai, Lithuania, June 1, 2022.

M. Radziunas, Steady states in dynamical semiconductor laser models and their analysis (online talk), 22nd International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD) (Online Event), September 12  16, 2022, Politecnico di Torino, Italy.

M. Wolfrum, Bumps, chimera states, and Turing patterns in systems of coupled active rotators, FrenchGerman WEHeraeusSeminar: Outstanding Challenges in Nonlinear Dynamics, March 20  25, 2022, Wilhelm und Else HeraeusStiftung, Les Houches, France, March 23, 2022.

M. Wolfrum, Dynamics of a stochastic excitable system with slowly adapting feedback (online tak), Adaptivity in nonlinear dynamical systems (Hybrid Event), September 20  23, 2022, PotsdamInstitute for Climate Impact Research, September 20, 2022.

M. Wolfrum, Dynamics of excitable units with noise and coupling, Nonlinear Science: Achievements and Perspectives, September 26  28, 2022, Universität Potsdam, September 28, 2022.

M. Wolfrum, Stability properties of temporal dissipative solitons in DDEs (online talk), Delay Days Utrecht 2022 (Hybrid Event), Hasselt University, Utrecht, Netherlands, May 12, 2022.

M. Wolfrum, Synchronization transitions in systems of coupled phase oscillators, Leibniz MMS Days 2022, April 25  27, 2022, PotsdamInstitut für Klimafolgenforschung (PIK), April 26, 2022.
External Preprints

L. Schülen, A. Gerdes, M. Wolfrum, A. Zakharova, The solitary route to chimera states, Preprint no. 2204.00385, Cornell University Library, arXiv.org, 2022, DOI /10.48550/arXiv.2204.00385 .
Abstract
We show how solitary states in a system of globally coupled FitzHughNagumo oscillators can lead to the emergence of chimera states. By a numerical bifurcation analysis of a suitable reduced system in the thermodynamic limit we demonstrate how solitary states, after emerging from the synchronous state, become chaotic in a perioddoubling cascade. Subsequently, states with a single chaotic oscillator give rise to states with an increasing number of incoherent chaotic oscillators. In large systems, these chimera states show extensive chaos. We demonstrate the coexistence of many of such chaotic attractors with different Lyapunov dimensions, due to different numbers of incoherent oscillators.
Research Groups
 Partial Differential Equations
 Laser Dynamics
 Numerical Mathematics and Scientific Computing
 Nonlinear Optimization and Inverse Problems
 Interacting Random Systems
 Stochastic Algorithms and Nonparametric Statistics
 Thermodynamic Modeling and Analysis of Phase Transitions
 Nonsmooth Variational Problems and Operator Equations