Extreme events in time-delayed nonlinear optics

Bosco, Andreas Karsaklian Dal; Wolfersberger, Delphine; Sciamanna, Marc

doi:10.1364/ol.38.000703

Cited by 57 publications

(16 citation statements)

References 11 publications

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“…By contrast, our time delay coupled FHN model does not exhibit such a distribution because the sizes of the extreme events are almost equal. Experimentally, extreme events containing chaotic small amplitude oscillations and large amplitude events have been found in a diode laser subject to a phase-conjugate feedback [28] and in a mode-locked fiber ring laser [43]. Though the experimental setups do not consider a coupling between two laser systems as studied here, they show some similarities to the dynamics studied.…”

Section: Discussionmentioning

confidence: 91%

“…In addition to the local interplay between nutrients and competing species, oceanic currents which transport nutrients and species from one region of blooming activity to another are also important factors shaping the dynamics and transport of blooms in the ocean [26,27]. In optical systems like lasers, rogue waves might be generated in systems where the finite travel time of signals may induce time delays [28]. Another example is neuronal communication between various regions of the brain which affect the levels of synchrony among these regions and lead to phenomena like epileptic seizures which are extreme events for the affected person [29,30].…”

Section: Introductionmentioning

confidence: 99%

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Extreme events in FitzHugh-Nagumo oscillators coupled with two time delays

Saha

Feudel

2017

Phys. Rev. E

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We study two identical FitzHugh-Nagumo oscillators which are coupled with one or two different time delays. If only a single-delay coupling is used, the length of the delay determines whether the synchronization manifold is transversally stable or unstable, exhibiting mixed-mode or chaotic oscillations in which the small amplitude oscillations are always in phase but the large amplitude oscillations are in phase or out of phase, respectively. For two delays we find an intricate dynamics which comprises an irregular alteration of small amplitude oscillations, in-phase and out-of-phase large amplitude oscillations, also called extreme events. This transient chaotic dynamics is sandwiched between a bubbling transition and a blowout bifurcation.

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Section: Discussionmentioning

confidence: 91%

Section: Introductionmentioning

confidence: 99%

Extreme events in FitzHugh-Nagumo oscillators coupled with two time delays

Saha

Feudel

2017

Phys. Rev. E

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“…1,2 . Due to their occurrence in a large class of physical systems [3][4][5][6] , a large body of research has been devoted to understanding such events in specific systems like rogue waves in oceans [7][8][9] and coupled laser systems [10][11][12][13] , harmful algal blooms in marine ecosystems 14,15 , epileptic seizures in the brain 16,17 and adverse weather conditions like floods, droughts and cyclones. Additionally, studies using theoretical models have shown that extreme events can be generated via various mechanisms including incoherent background of interacting waves 18 , noise-induced attractor hopping 19,20 , pulse-coupled small world networks 21 , inhomogeneous networks of oscillators 1,2 and delay coupled relaxation oscillators 22 .…”

Section: Introductionmentioning

confidence: 99%

Riddled basins of attraction in systems exhibiting extreme events

Saha

Feudel

2018

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Using a system of two FitzHugh-Nagumo units, we demonstrate the occurrence of riddled basins of attraction in delay-coupled systems as the coupling between the units is increased. We characterize riddled basins using the uncertainty exponent which is a measure of the dimensions of the basin boundary. Additionally, we show that the phase space can be partitioned into pure and mixed regions, where initial conditions in the pure regions certainly avoid the generation of extreme events, while initial conditions in the mixed region may or may not exhibit such events. This implies that any tiny perturbation of initial conditions in the mixed region could yield the emergence of extreme events because the latter state possesses a riddled basin of attraction.

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“…This condition has recently been questioned for the case of ocean waves [22]. Other nonlinear scenarios associated with EE formation include chaotic dynamics in lowdimensional systems [23], stochastically induced transitions in multistable systems [24], collisions of breather-solitons [25], integrable turbulence [26], spatiotemporal chaos [27], vortex dynamics [28], vortex turbulence [29], and delayed-feedback systems [30,31]. In the case of low-dimensional chaotic systems, crises have been identified as one of the mechanisms associated with the emergency of EEs [32], and they have recently received some attention [33][34][35].…”

Section: Introductionmentioning

confidence: 99%

Extreme and superextreme events in a loss-modulatedCO2laser: Nonlinear resonance route and precursors

Bonatto

Endler

2017

Phys. Rev. E

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We investigate the occurrence of extreme and rare events, i.e., giant and rare light pulses, in a periodically modulated CO_{2} laser model. Due to nonlinear resonant processes, we show a scenario of interaction between chaotic bands of different orders, which may lead to the formation of extreme and rare events. We identify a crisis line in the modulation parameter space, and we show that, when the modulation amplitude increases, remaining in the vicinity of the crisis, some statistical properties of the laser pulses, such as the average and dispersion of amplitudes, do not change much, whereas the amplitude of extreme events grows enormously, giving rise to extreme events with much larger deviations than usually reported, with a significant probability of occurrence, i.e., with a long-tailed non-Gaussian distribution. We identify recurrent regular patterns, i.e., precursors, that anticipate the emergence of extreme and rare events, and we associate these regular patterns with unstable periodic orbits embedded in a chaotic attractor. We show that the precursors may or may not lead to the emergence of extreme events. Thus, we compute the probability of success or failure (false alarm) in the prediction of the extreme events, once a precursor is identified in the deterministic time series. We show that this probability depends on the accuracy with which the precursor is identified in the laser intensity time series.

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Extreme events in time-delayed nonlinear optics

Cited by 57 publications

References 11 publications

Extreme events in FitzHugh-Nagumo oscillators coupled with two time delays

Extreme events in FitzHugh-Nagumo oscillators coupled with two time delays

Riddled basins of attraction in systems exhibiting extreme events

Extreme and superextreme events in a loss-modulatedCO2laser: Nonlinear resonance route and precursors

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