Changing Dynamical Complexity with Time Delay in Coupled Fiber Laser Oscillators

Franz, Anthony L.; Roy, Rajarshi; Shaw, Leah B.; Schwartz, Ira B.

doi:10.1103/physrevlett.99.053905

Cited by 17 publications

(12 citation statements)

References 19 publications

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“…That is, the cross correlation between the two lasers peaks not at zero, but at lag time equal to the delay. This has also been observed in two laser systems [19,21]. The theoretical analysis of this will be presented elsewhere for the fiber ring lasers in the hub formation.…”

Section: Resultssupporting

confidence: 52%

“…Previous work has also considered noise-induced synchronization in EDFRLs connected via passive coupling delay lines. For two coupled lasers of this type, both modeling and experimentation have demonstrated a complex "leader-follower" phenomenon of dynamic achronal synchronization between the two lasers, where the offset of the phase is precisely equal to the delay time introduced by the passive coupling line [19][20][21]. In the case of the two coupled fiber ring lasers, the achronal synchronization is observed to be non-stationary in both theory and experiment, since leading and lagging lasers switch roles over the course of long time observations.…”

Section: Introductionmentioning

confidence: 99%

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Modeling synchronization in networks of delay-coupled fiber ring lasers

Lindley¹,

Schwartz²

2011

Opt. Express

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We study the onset of synchronization in a network of N delay-coupled stochastic fiber ring lasers with respect to various parameters when the coupling power is weak. In particular, for groups of three or more ring lasers mutually coupled to a central hub laser, we demonstrate a robust tendency toward out-of-phase (achronal) synchronization between the N-1 outer lasers and the single inner laser. In contrast to the achronal synchronization, we find the outer lasers synchronize with zero-lag (isochronal) with respect to each other, thus forming a set of N-1 coherent fiber lasers.

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Section: Resultssupporting

confidence: 52%

Section: Introductionmentioning

confidence: 99%

Modeling synchronization in networks of delay-coupled fiber ring lasers

Lindley¹,

Schwartz²

2011

Opt. Express

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“…The internal selffeedback delay could also be induced by a finite reaction time, which may be given dynamically by the inertia of the local dynamical system without including an explicit delay term, such as the cavity delay time that is often negligible in the laser systems. However, the particular topological structure of a ring of coupled fiber lasers explicitly gives rise to this intrinsic self-feedback delay, 53 where the external coupling delay is emphasized to be induced by a certain time of signal propagation, and the local self-feedback delay arises as an internal round-trip time for the light. So far, there still lacks a clear discrimination between them in regulating collective dynamics.…”

Section: Introductionmentioning

confidence: 99%

Revival of oscillations from deaths in diffusively coupled nonlinear systems: Theory and experiment

Zou

Šebek

Kiss

et al. 2017

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Amplitude death (AD) and oscillation death (OD) are two structurally different oscillation quenching phenomena in coupled nonlinear systems. As a reverse issue of AD and OD, revival of oscillations from deaths attracts an increasing attention recently. In this paper, we clearly disclose that a time delay in the self-feedback component of the coupling destabilizes not only AD but also OD, and even the AD to OD transition in paradigmatic models of coupled Stuart-Landau oscillators under diverse death configurations. Using a rigorous analysis, the effectiveness of this self-feedback delay in revoking AD is theoretically proved to be valid in an arbitrary network of coupled Stuart-Landau oscillators with generally distributed propagation delays. Moreover, the role of self-feedback delay in reviving oscillations from AD is experimentally verified in two delay-coupled electrochemical reactions.

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“…Refs. [1][2][3][4][5][6][7][8]. Another example is Josephson junctions coupled to shunting transmission lines [9,10].…”

Section: Introductionmentioning

confidence: 99%

Noise-induced switching and extinction in systems with delay

et al. 2015

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We consider the rates of noise-induced switching between the stable states of dissipative dynamical systems with delay and also the rates of noise-induced extinction, where such systems model population dynamics. We study a class of systems where the evolution depends on the dynamical variables at a preceding time with a fixed time delay, which we call hard delay. For weak noise, the rates of interattractor switching and extinction are exponentially small. Finding these rates to logarithmic accuracy is reduced to variational problems. The solutions of the variational problems give the most probable paths followed in switching or extinction. We show that the equations for the most probable paths are acausal and formulate the appropriate boundary conditions. Explicit results are obtained for small delay compared to the relaxation rate. We also develop a direct variational method to find the rates. We find that the analytical results agree well with the numerical simulations for both switching and extinction rates.

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Changing Dynamical Complexity with Time Delay in Coupled Fiber Laser Oscillators

Cited by 17 publications

References 19 publications

Modeling synchronization in networks of delay-coupled fiber ring lasers

Modeling synchronization in networks of delay-coupled fiber ring lasers

Revival of oscillations from deaths in diffusively coupled nonlinear systems: Theory and experiment

Noise-induced switching and extinction in systems with delay

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