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Sahay A, Kushwaha A, Pawar SA, P R M, Dhadphale JM, Sujith RI. Mitigation of limit cycle oscillations in a turbulent thermoacoustic system via delayed acoustic self-feedback. CHAOS (WOODBURY, N.Y.) 2023; 33:043118. [PMID: 37097926 DOI: 10.1063/5.0129512] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/05/2022] [Accepted: 03/15/2023] [Indexed: 06/19/2023]
Abstract
We report the occurrence of amplitude death (AD) of limit cycle oscillations in a bluff body stabilized turbulent combustor through delayed acoustic self-feedback. Such feedback control is achieved by coupling the acoustic field of the combustor to itself through a single coupling tube attached near the anti-node position of the acoustic standing wave. We observe that the amplitude and dominant frequency of the limit cycle oscillations gradually decrease as the length of the coupling tube is increased. Complete suppression (AD) of these oscillations is observed when the length of the coupling tube is nearly 3 / 8 times the wavelength of the fundamental acoustic mode of the combustor. Meanwhile, as we approach this state of amplitude death, the dynamical behavior of acoustic pressure changes from the state of limit cycle oscillations to low-amplitude chaotic oscillations via intermittency. We also study the change in the nature of the coupling between the unsteady flame dynamics and the acoustic field as the length of the coupling tube is increased. We find that the temporal synchrony between these oscillations changes from the state of synchronized periodicity to desynchronized aperiodicity through intermittent synchronization. Furthermore, we reveal that the application of delayed acoustic self-feedback with optimum feedback parameters completely disrupts the positive feedback loop between hydrodynamic, acoustic, and heat release rate fluctuations present in the combustor during thermoacoustic instability, thus mitigating instability. We anticipate this method to be a viable and cost-effective option to mitigate thermoacoustic oscillations in turbulent combustion systems used in practical propulsion and power systems.
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Affiliation(s)
- Ankit Sahay
- Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai, Tamil Nadu 600036, India
| | - Abhishek Kushwaha
- Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai, Tamil Nadu 600036, India
| | - Samadhan A Pawar
- Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai, Tamil Nadu 600036, India
| | - Midhun P R
- Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai, Tamil Nadu 600036, India
| | - Jayesh M Dhadphale
- Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai, Tamil Nadu 600036, India
| | - R I Sujith
- Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai, Tamil Nadu 600036, India
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2
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Galler M, Lüdge K, Humphries R, Mulchrone K, Hövel P. Deterministic and stochastic effects in spreading dynamics: A case study of bovine viral diarrhea. CHAOS (WOODBURY, N.Y.) 2021; 31:093129. [PMID: 34598439 DOI: 10.1063/5.0058688] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/01/2021] [Accepted: 08/16/2021] [Indexed: 06/13/2023]
Abstract
Bovine viral diarrhea (BVD) is a disease in cattle with complex transmission dynamics that causes substantial economic losses and affects animal welfare. The infection can be transient or persistent. The mostly asymptomatic persistently infected hosts are the main source for transmission of the virus. This characteristic makes it difficult to control the spreading of BVD. We develop a deterministic compartmental model for the spreading dynamics of BVD within a herd and derive the basic reproduction number. This epidemiological quantity indicates that identification and removal of persistently infected animals is a successful control strategy if the transmission rate of transiently infected animals is small. Removing persistently infected animals from the herd at birth results in recurrent outbreaks with decreasing peak prevalence. We propose a stochastic version of the compartmental model that includes stochasticity in the transmission parameters. This stochasticity leads to sustained oscillations in cases where the deterministic model predicts oscillations with decreasing amplitude. The results provide useful information for the design of control strategies.
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Affiliation(s)
- Markus Galler
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
| | - Kathy Lüdge
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
| | - Rory Humphries
- School of Mathematical Sciences, University College Cork, Western Road, Cork T12 XF64, Ireland
| | - Kieran Mulchrone
- School of Mathematical Sciences, University College Cork, Western Road, Cork T12 XF64, Ireland
| | - Philipp Hövel
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
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3
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González Ochoa HO, Perales GS, Epstein IR, Femat R. Effects of stochastic time-delayed feedback on a dynamical system modeling a chemical oscillator. Phys Rev E 2018; 97:052214. [PMID: 29906855 DOI: 10.1103/physreve.97.052214] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/10/2018] [Indexed: 06/08/2023]
Abstract
We examine how stochastic time-delayed negative feedback affects the dynamical behavior of a model oscillatory reaction. We apply constant and stochastic time-delayed negative feedbacks to a point Field-Körös-Noyes photosensitive oscillator and compare their effects. Negative feedback is applied in the form of simulated inhibitory electromagnetic radiation with an intensity proportional to the concentration of oxidized light-sensitive catalyst in the oscillator. We first characterize the system under nondelayed inhibitory feedback; then we explore and compare the effects of constant (deterministic) versus stochastic time-delayed feedback. We find that the oscillatory amplitude, frequency, and waveform are essentially preserved when low-dispersion stochastic delayed feedback is used, whereas small but measurable changes appear when a large dispersion is applied.
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Affiliation(s)
- Héctor O González Ochoa
- Departamento de Electrónica, Universidad de Guadalajara. Av. Revolución 1500, 44430, Guadalajara Jal, México
| | - Gualberto Solís Perales
- Departamento de Electrónica, Universidad de Guadalajara. Av. Revolución 1500, 44430, Guadalajara Jal, México
| | - Irving R Epstein
- Department of Chemistry, Brandeis University, Waltham, Massachusetts 02454-9110, USA
| | - Ricardo Femat
- Instituto Potosino de Investigación Científica y Tecnológica A.C., San Luis Potosí, México
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Jaurigue L, Schöll E, Lüdge K. Suppression of Noise-Induced Modulations in Multidelay Systems. PHYSICAL REVIEW LETTERS 2016; 117:154101. [PMID: 27768335 DOI: 10.1103/physrevlett.117.154101] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/23/2016] [Indexed: 06/06/2023]
Abstract
Many physical systems involve time-delayed feedback or coupling. In such delay systems, noise can give rise to undesirable oscillations at frequencies resonant to the delay times. We investigate how an additional feedback term can suppress noise-induced modulations in delay systems with self-feedback that exhibit deterministic oscillatory dynamics. A simple characteristic equation is derived to predict optimal delay times for the prototypical example of a Stuart-Landau oscillator subject to two feedback terms. We then show that a characteristic equation of the same form accurately describes the dominant Floquet modes of more complex oscillatory systems and hence can be used to optimize the suppression of noise-induced modulations. This is shown for mode-locked lasers and FitzHugh-Nagumo oscillators subject to self-feedback.
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Affiliation(s)
- Lina Jaurigue
- Institut für Theoretische Physik, Sekretariat EW 7-1, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
| | - Eckehard Schöll
- Institut für Theoretische Physik, Sekretariat EW 7-1, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
| | - Kathy Lüdge
- Institut für Theoretische Physik, Sekretariat EW 7-1, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
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5
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Gjurchinovski A, Zakharova A, Schöll E. Amplitude death in oscillator networks with variable-delay coupling. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:032915. [PMID: 24730921 DOI: 10.1103/physreve.89.032915] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/29/2013] [Indexed: 06/03/2023]
Abstract
We study the conditions of amplitude death in a network of delay-coupled limit cycle oscillators by including time-varying delay in the coupling and self-feedback. By generalizing the master stability function formalism to include variable-delay connections with high-frequency delay modulations (i.e., the distributed-delay limit), we analyze the regimes of amplitude death in a ring network of Stuart-Landau oscillators and demonstrate the superiority of the proposed method with respect to the constant delay case. The possibility of stabilizing the steady state is restricted by the odd-number property of the local node dynamics independently of the network topology and the coupling parameters.
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Affiliation(s)
- Aleksandar Gjurchinovski
- Institute of Physics, Faculty of Natural Sciences and Mathematics, Sts. Cyril and Methodius University, P. O. Box 162, 1000 Skopje, Macedonia
| | - Anna Zakharova
- Institut für Theoretische Physik, Technische Universität Berlin, 10623 Berlin, Germany
| | - Eckehard Schöll
- Institut für Theoretische Physik, Technische Universität Berlin, 10623 Berlin, Germany
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6
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Selivanov AA, Lehnert J, Dahms T, Hövel P, Fradkov AL, Schöll E. Adaptive synchronization in delay-coupled networks of Stuart-Landau oscillators. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:016201. [PMID: 22400637 DOI: 10.1103/physreve.85.016201] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/01/2011] [Revised: 11/01/2011] [Indexed: 05/31/2023]
Abstract
We consider networks of delay-coupled Stuart-Landau oscillators. In these systems, the coupling phase has been found to be a crucial control parameter. By proper choice of this parameter one can switch between different synchronous oscillatory states of the network. Applying the speed-gradient method, we derive an adaptive algorithm for an automatic adjustment of the coupling phase such that a desired state can be selected from an otherwise multistable regime. We propose goal functions based on both the difference of the oscillators and a generalized order parameter and demonstrate that the speed-gradient method allows one to find appropriate coupling phases with which different states of synchronization, e.g., in-phase oscillation, splay, or various cluster states, can be selected.
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Affiliation(s)
- Anton A Selivanov
- Department of Theoretical Cybernetics, Saint-Petersburg State University, Saint-Petersburg, Russia
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Flunkert V, Schöll E. Towards easier realization of time-delayed feedback control of odd-number orbits. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:016214. [PMID: 21867280 DOI: 10.1103/physreve.84.016214] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/01/2011] [Indexed: 05/31/2023]
Abstract
We develop generalized time-delayed feedback schemes for the stabilization of periodic orbits with an odd number of positive Floquet exponents, which are particularly well suited for experimental realization. We construct the parameter regimes of successful control and validate these by numerical simulations and numerical continuation methods. In particular, it is shown how periodic orbits can be stabilized with symmetric feedback matrices by introducing an additional latency time in the control loop. Finally, we show using normal form analysis and numerical simulations how our results could be implemented in a laser setup using optoelectronic feedback.
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Affiliation(s)
- V Flunkert
- Institut für Theoretische Physik, Technische Universität Berlin, Berlin, Germany.
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Hinz RC, Hövel P, Schöll E. Transient behavior in systems with time-delayed feedback. CHAOS (WOODBURY, N.Y.) 2011; 21:023114. [PMID: 21721756 DOI: 10.1063/1.3581161] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
We investigate the transient times for the onset of control of steady states by time-delayed feedback. The optimization of control by minimizing the transient time before control becomes effective is discussed analytically and numerically, and the competing influences of local and global features are elaborated. We derive an algebraic scaling of the transient time and confirm our findings by numerical simulations in dependence on feedback gain and time delay.
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Affiliation(s)
- Robert C Hinz
- Institut für Theoretische Physik, TU Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
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Fiedler B, Flunkert V, Hövel P, Schöll E. Delay stabilization of periodic orbits in coupled oscillator systems. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2010; 368:319-341. [PMID: 20008404 DOI: 10.1098/rsta.2009.0232] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
We study diffusively coupled oscillators in Hopf normal form. By introducing a non-invasive delay coupling, we are able to stabilize the inherently unstable anti-phase orbits. For the super- and subcritical cases, we state a condition on the oscillator's nonlinearity that is necessary and sufficient to find coupling parameters for successful stabilization. We prove these conditions and review previous results on the stabilization of odd-number orbits by time-delayed feedback. Finally, we illustrate the results with numerical simulations.
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Affiliation(s)
- B Fiedler
- Institut für Mathematik I, Free Universität Berlin, Arnimallee 2-6, 14195 Berlin, Germany
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Brandstetter S, Dahlem MA, Schöll E. Interplay of time-delayed feedback control and temporally correlated noise in excitable systems. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2010; 368:391-421. [PMID: 20008408 DOI: 10.1098/rsta.2009.0233] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
The interplay of time-delayed feedback and temporally correlated coloured noise in a single and two coupled excitable systems is studied in the framework of the FitzHugh-Nagumo (FHN) model. By using coloured noise instead of white noise, the noise correlation time is introduced as an additional time scale. We show that in a single FHN system the major time scale of oscillations is strongly influenced by the noise correlation time, which in turn affects the maxima of coherence with respect to the delay time. In two coupled FHN systems, coloured noise input to one subsystem influences coherence resonance and stochastic synchronization of both subsystems. Application of delayed feedback control to the coloured noise-driven subsystem is shown to change coherence and time scales of noise-induced oscillations in both systems, and to enhance or suppress stochastic synchronization under certain conditions.
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Affiliation(s)
- S Brandstetter
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, D-10623 Berlin, Germany
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Pototsky A, Janson NB. Delay-induced spatial correlations in one-dimensional stochastic networks with nearest-neighbor coupling. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 80:066203. [PMID: 20365250 DOI: 10.1103/physreve.80.066203] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/08/2009] [Indexed: 05/29/2023]
Abstract
We consider a network of deterministic and stochastic locally coupled oscillators with positive or negative dissipation and local time-delayed feedback. (i) For a deterministic system, we study propagation of waves through the network. We show that time delay leads to a coexistence of several neutral modes with different wave numbers and group velocities, which we compute analytically. (ii) For noisy system, we study the response of the network to external random forcing correlated in space and uncorrelated in time. Below the threshold of spatial instability, noise induces spatiotemporal fluctuations, which can be characterized by the structure function. We give an analytical expression for the structure function and demonstrate the effect of the time delay and of the correlation length of noise on the wave number of the most excited mode.
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Affiliation(s)
- Andrey Pototsky
- Department of Mathematical Sciences, Loughborough University, Leicestershire, United Kingdom
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Schöll E, Hiller G, Hövel P, Dahlem MA. Time-delayed feedback in neurosystems. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2009; 367:1079-96. [PMID: 19218152 DOI: 10.1098/rsta.2008.0258] [Citation(s) in RCA: 33] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Abstract
The influence of time delay in systems of two coupled excitable neurons is studied in the framework of the FitzHugh-Nagumo model. A time delay can occur in the coupling between neurons or in a self-feedback loop. The stochastic synchronization of instantaneously coupled neurons under the influence of white noise can be deliberately controlled by local time-delayed feedback. By appropriate choice of the delay time, synchronization can be either enhanced or suppressed. In delay-coupled neurons, antiphase oscillations can be induced for sufficiently large delay and coupling strength. The additional application of time-delayed self-feedback leads to complex scenarios of synchronized in-phase or antiphase oscillations, bursting patterns or amplitude death.
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Affiliation(s)
- Eckehard Schöll
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, 10623 Berlin, Germany.
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Time-Delayed Feedback Control: From Simple Models to Lasers and Neural Systems. UNDERSTANDING COMPLEX SYSTEMS 2009. [DOI: 10.1007/978-3-642-02329-3_4] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/11/2023]
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Hizanidis J, Schöll E. Control of coherence resonance in semiconductor superlattices. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:066205. [PMID: 19256923 DOI: 10.1103/physreve.78.066205] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/29/2008] [Revised: 10/13/2008] [Indexed: 05/27/2023]
Abstract
We study the effect of time-delayed feedback control and Gaussian white noise on the spatiotemporal charge dynamics in a semiconductor superlattice. The system is prepared in a regime where the deterministic dynamics is close to a global bifurcation, namely, a saddle-node bifurcation on a limit cycle. In the absence of control, noise can induce electron charge front motion through the entire device, and coherence resonance is observed. We show that with appropriate selection of the time-delayed feedback parameters the effect of coherence resonance can be either enhanced or destroyed, and the coherence of stochastic domain motion at low noise intensity is dramatically increased. Additionally, the purely delay-induced dynamics in the system is investigated, and a homoclinic bifurcation of a limit cycle is found.
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Affiliation(s)
- Johanne Hizanidis
- Instutut für Theoretische Physik, Technische Universität Berlin, Hardenbergstasse 36, D-10623 Berlin, Germany
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Dahms T, Hövel P, Schöll E. Stabilizing continuous-wave output in semiconductor lasers by time-delayed feedback. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:056213. [PMID: 19113206 DOI: 10.1103/physreve.78.056213] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/22/2008] [Indexed: 05/27/2023]
Abstract
The stabilization of steady states is studied in a modified Lang-Kobayashi model of a semiconductor laser. We show that multiple time-delayed feedback, realized by a Fabry-Perot resonator coupled to the laser, provides a valuable tool for the suppression of unwanted intensity pulsations, and leads to stable continuous-wave operation. The domains of control are calculated in dependence on the feedback strength, delay time (cavity round trip time), memory parameter (mirror reflectivity), latency time, feedback phase, and bandpass filtering. Due to the optical feedback, multistable behavior can also occur in the form of delay-induced intensity pulsations or other modes for certain choices of the control parameters. Control may then still be achieved by slowly ramping the injection current during turn-on.
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Affiliation(s)
- Thomas Dahms
- Institut für Theoretische Physik, Technische Universität Berlin, 10623 Berlin, Germany
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