Chaos synchronization in networks of delay-coupled lasers: role of the coupling phases

Flunkert, Valentín; Schöll, Eckehard

doi:10.1088/1367-2630/14/3/033039

Cited by 26 publications

(25 citation statements)

References 50 publications

(91 reference statements)

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“…Our understanding and treatment of various brain pathologies and deficiencies, such as Parkinson's, Alzheimer's and epilepsy, relies heavily on the analysis of synchronization of oscillating neural populations [3][4][5]. Recent work on laser communication networks has extensively used coupled oscillator models to study the dynamics of in-phase or anti-phase and complete chaos synchronization [6][7][8][9][10]. Chimera states, where a network of oscillators splits into coexisting domains of coherent, phaselocked and incoherent, desynchronized behaviour, have also been observed [11][12][13][14][15].…”

Section: Introductionmentioning

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: Introductionmentioning

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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“…The aim of the present study is to provide a bridge between laser networks and chimera patterns, which opens up numerous perspectives for application of chimera states and at the same time provides more insight into their understanding on the conceptual level. While synchronization phenomena have been well studied for small networks of coupled laser systems [37][38][39][40][41][42], chimera states have not yet been reported in laser networks so far. This sparks the question what conditions have to be met for the formation of chimera states in laser networks.…”

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confidence: 99%

Amplitude-phase coupling drives chimera states in globally coupled laser networks

et al. 2015

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For a globally coupled network of semiconductor lasers with delayed optical feedback, we demonstrate the existence of chimera states. The domains of coherence and incoherence that are typical for chimera states are found to exist for the amplitude, phase, and inversion of the coupled lasers. These chimera states defy several of the previously established existence criteria. While chimera states in phase oscillators generally demand nonlocal coupling, large system sizes, and specially prepared initial conditions, we find chimera states that are stable for global coupling in a network of only four coupled lasers for random initial conditions. The existence is linked to a regime of multistability between the synchronous steady state and asynchronous periodic solutions. We show that amplitude-phase coupling, a concept common in different fields, is necessary for the formation of the chimera states. Synchronization is a common phenomenon in interacting nonlinear dynamical systems in various fields of research such as physics, chemistry, biology, engineering, or socioeconomic sciences [1][2][3]. While a lot of knowledge has been gained on the origin of complete synchronization, more complex partial synchronization patterns have only recently become the focus of intense research. We still lack a full understanding of these phenomena, and a very prominent example are chimera states where an ensemble of identical elements self-organizes into spatially separated coexisting domains of coherent (synchronized) and incoherent (desynchronized) dynamics [4,5]. Since their first discovery a decade ago many theoretical investigations of coupled phase oscillators and other simplified models have been carried out [6,7] [7,16,17], e.g., spiral wave chimeras [18,19], FitzHugh-Nagumo neural systems [20], Stuart-Landau oscillators [21][22][23], where pure amplitude chimeras [24] were found, or quantum interference devices [25]. In real-world systems chimera states might play a role, e.g., in the unihemispheric sleep of birds and dolphins [26], in neuronal bump states [27,28], in power grids [29], or in social systems [30].Although no universal mechanism for the formation of chimera states has yet been established, three general essential requirements have been found in many studies: (i) a large number of coupled elements, (ii) non-local coupling, and (iii) specific initial conditions. These were primarily derived from the phase oscillator model [7] but also apply to other systems. If these conditions are not met, the chimera states tend to have very short lifetimes. Recent studies, however, suggest that these paradigms can be broken and chimera states are observed also for small system sizes [31], global coupling [15,23,32,33] and random initial conditions [34].Surprisingly, chimera states appear at the interface of independent fields of research putting together different scientific communities. Recent examples are quantum chimera state [35] or coexistence of coherent and incoherent patterns with respect to the modes of an optical com...

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“…We will illustrate the analysis for motif (ii). For the other motifs, the analysis is similar, albeit it might be more involved [5].…”

Section: Two Lasersmentioning

confidence: 99%

“…The aim of this contribution is to derive synchronization conditions for all-optically coupled laser networks [4,5]. For our stability analysis we employ recent results concerning the master stability function (MSF) [9] in the limit of large delay times [6,7].…”

Section: Introductionmentioning

confidence: 99%

Chaos and Synchronization in Delayed System : Applications to Laser Networks

Flunkert

Schöll

2013

ESAIM: Proc.

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Abstract. We discuss recent results on chaos synchronization of delayed systems. We investigate the limit of large coupling delays and discuss how in this limit the stability problem for the synchronized solution is drastically simplified. We use these results to derive rigorous conditions for chaos synchronization of all-optically coupled laser networks. In laser systems the optical coupling phases have to be taken into account and give rise to interference conditions. We show that the relative phases between lasers can be used to optimize the effective coupling matrix.

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Chaos synchronization in networks of delay-coupled lasers: role of the coupling phases

Cited by 26 publications

References 50 publications

Amplitude and phase dynamics in oscillators with distributed-delay coupling

Amplitude and phase dynamics in oscillators with distributed-delay coupling

Amplitude-phase coupling drives chimera states in globally coupled laser networks

Chaos and Synchronization in Delayed System : Applications to Laser Networks

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