Synchronization of Delay-Coupled Oscillators: A Study of Semiconductor Lasers

Hj, Wünsche; Bauer, S.; Kreissl, J.; Ушаков, О. В.; Korneyev, Nikolay; Henneberger, F.; Wille, Eric; Erzgräber, Hartmut; Peil, Michael; Elsäßer, Wolfgang; Fischer, Ingo

doi:10.1103/physrevlett.94.163901

Cited by 129 publications

(80 citation statements)

References 11 publications

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“…Another possibility would be to consider whether coupled systems with delay-distributed coupling are able to exhibit other types of phase dynamics and synchronization. One such scenario, which is useful in laser applications, is the case when the sum of the phases of the two oscillators is constant [29,86]. Phase approximation in this case results in a delayed Adler equation, and it would be both theoretically and practically important to consider possible solutions of this model for different delay distributions.…”

Section: Discussionmentioning

confidence: 99%

Amplitude and phase dynamics in oscillators with distributed-delay coupling

Kyrychko

Blyuss

Schöll

2013

Phil. Trans. R. Soc. A.

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This paper studies the effects of distributed-delay coupling on the dynamics in a system of non-identical coupled Stuart–Landau oscillators. For uniform and gamma delay distribution kernels, the conditions for amplitude death are obtained in terms of average frequency, frequency detuning and the parameters of the coupling, including coupling strength and phase, as well as the mean time delay and the width of the delay distribution. To gain further insights into the dynamics inside amplitude death regions, the eigenvalues of the corresponding characteristic equations are computed numerically. Oscillatory dynamics of the system is also investigated, using amplitude and phase representation. Various branches of phase-locked solutions are identified, and their stability is analysed for different types of delay distributions.

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Section: Discussionmentioning

confidence: 99%

Amplitude and phase dynamics in oscillators with distributed-delay coupling

Kyrychko

Blyuss

Schöll

2013

Phil. Trans. R. Soc. A.

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“…[9,13]. For a short delay time of τ ≈ ν −1 RO regular dynamics, such as frequency locking with continuous wave emission and regular intensity oscillations, are domin-ant [14][15][16]. Depending on the detuning between the two lasers, a characteristic scenario has recently been demonstrated [16].…”

Section: Introductionmentioning

confidence: 99%

“…[20][21][22] as entry points to the extensive literature on the subject. Phenomena that are attributed to time-delayed coupling include multistabilities, amplitude death and the onset of delay-induced instabilities [23,3,2,16].…”

Section: Introductionmentioning

confidence: 99%

Mutually delay-coupled semiconductor lasers: Mode bifurcation scenarios

Erzgräber

Lenstra

Krauskopf

et al. 2005

Optics Communications

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We study the spectral and dynamical behavior of two identical, mutually delaycoupled semiconductor lasers. We concentrate on the short coupling-time regime where the number of basic states of the system, the compound laser modes (CLMs), is small so that their individual behavior can be studied both experimentally and theoretically. As such it constitutes a prototype example of delay-coupled laser systems, which play an important role, e.g., in telecommunication.Specifically, for small spectral detuning we find several stable CLMs of the coupled system where both lasers lock onto a common frequency and emit continuous wave output. A bifurcation analysis of the CLMs in the full rate equation model with delay reveals the structure of stable and unstable CLMs. We find a characteristic bifurcation scenario as a function of the detuning and the coupling phase between the two lasers that explains experimentally observed multistabilities and mode jumps in the locking region.

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“…These time lags give rise to complex dynamics and have been shown to play a key role in the synchronization behaviour of neural systems (Hauschildt et al 2006;Gassel et al 2007;Dahlem et al 2009;Schöll et al 2009). Coupled lasers exhibit similar phenomena to coupled neurons and have attracted much attention owing to their importance in telecommunication applications (Wünsche et al 2005;Fischer et al 2006;Klein et al 2006;Shaw et al 2006;Landsman & Schwartz 2007;Flunkert et al 2009). For many technological and medical applications, non-invasive methods of control are desirable as they have no side effects and do not compromise the performance of the controlled system.…”

Section: Introductionmentioning

confidence: 99%

Delay stabilization of periodic orbits in coupled oscillator systems

Fiedler

Flunkert

Hövel

et al. 2010

Phil. Trans. R. Soc. A.

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We study diffusively coupled oscillators in Hopf normal form. By introducing a noninvasive 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 oddnumber orbits by time-delayed feedback. Finally, we illustrate the results with numerical simulations.

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Synchronization of Delay-Coupled Oscillators: A Study of Semiconductor Lasers

Cited by 129 publications

References 11 publications

Amplitude and phase dynamics in oscillators with distributed-delay coupling

Amplitude and phase dynamics in oscillators with distributed-delay coupling

Mutually delay-coupled semiconductor lasers: Mode bifurcation scenarios

Delay stabilization of periodic orbits in coupled oscillator systems

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