Dragon-king extreme events as precursors for catastrophic transition

Premraj, D.; Kumarasamy, Suresh; Pawar, Samadhan A.; Kabiraj, Lipika; Prasad, Awadhesh; Sujith, R. I.

doi:10.1209/0295-5075/134/34006

“…These states include period-2, period-3, periodk, frequency-locked, quasiperiodic, strange nonchaotic, intermittent, and chaotic oscillations. There are many experimental as well as theoretical studies in the thermoacoustic literature that report the existence of these dynamical behaviors in Rijke tube systems 74,75,109,110,150,[177][178][179][180] . Sometimes, a secondary Hopf bifurcation observed due to a change in the control parameter leads to the transition from low amplitude limit cycle oscillations to high amplitude limit cycle oscillations, where both the limit cycle oscillations exhibit the same frequency 28 .…”

Section: Secondary Hopf Bifurcations In Thermoacoustic Systemsmentioning

confidence: 99%

“…This novel methodology does not involve the crossing of threshold values (unlike other measures discussed before) and can be applied to various other dynamical systems that exhibit a Hopf bifurcation (or systems that can be reduced to Stuart-Landau equations). Premraj et al 180 investigated the occurrence of a catastrophic transition, such as flame blowout, in a laminar premixed Rijke tube burner. During flame blowout, the flame ceases to exist in the combustor as the time scales of flow fluctuations become much larger than the reaction timescales in the system.…”

Section: Early Warning Signals (Precursors)mentioning

confidence: 99%

“…After the flame blowout, the amplitude of the acoustic pressure fluctuations in the system drops to a very low value. Premraj et al 180 noticed that the occurrence of flame blowout is preceded by the existence of extreme events in the acoustic field of the system and found the presence of special kind of extreme events called the dragon-king extreme events just prior to flame blowout. Thus, the early warning to flame blowout can be provided by identifying the dragon-king extreme events in the acoustic field of the system.…”

Section: Early Warning Signals (Precursors)mentioning

confidence: 99%

See 1 more Smart Citation

Rijke tube: A nonlinear oscillator

Manoj,

Pawar,

Kurths

et al. 2022

Preprint

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0

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Dynamical systems theory has emerged as an interdisciplinary area of research to characterize the complex dynamical transitions in real-world systems. Various nonlinear dynamical phenomena and bifurcations have been discovered over the decades using different reduced-order models of oscillators. Different measures and methodologies have been developed theoretically to detect, control, or suppress the nonlinear oscillations. However, obtaining such phenomena experimentally is often challenging, time-consuming, and risky, mainly due to the limited control of certain parameters during experiments. With this review, we aim to introduce a paradigmatic and easily configurable Rijke tube oscillator to the dynamical systems community. The Rijke tube is commonly used by the combustion community as a prototype to investigate the detrimental phenomena of thermoacoustic instability. Recent investigations in such Rijke tubes have utilized various methodologies from dynamical systems theory to better understand the occurrence of thermoacoustic oscillations, their prediction and mitigation, both experimentally and theoretically. The existence of various dynamical behaviors has been reported in single as well as coupled Rijke tube oscillators. These behaviors include bifurcations, routes to chaos, noise-induced transitions, synchronization, and suppression of oscillations. Various early warning measures have been established to predict thermoacoustic instabilities. Therefore, this review paper consolidates the usefulness of a Rijke tube oscillator in terms of experimentally discovering and modeling different nonlinear phenomena observed in physics; thus, transcending the boundaries between the physics and the engineering communities.

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“…The search for dynamical systems that yield extreme events, without the drive of external stochastic influences or intrinsic random fluctuations, is a focus of much ongoing research effort from the point of view of basic understanding of complex systems 14 – 17 . Additionally, such probabilistic outcomes in dynamical systems are most relevant in the applied context as well, such as in engineering sciences where this direction of research leads to better assessment of risks 18 .…”

Section: Introductionmentioning

confidence: 99%

Enhancement of extreme events through the Allee effect and its mitigation through noise in a three species system

Sen

¹

,

Sinha

²

2021

Sci Rep

2

0

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We consider the dynamics of a three-species system incorporating the Allee Effect, focussing on its influence on the emergence of extreme events in the system. First we find that under Allee effect the regular periodic dynamics changes to chaotic. Further, we find that the system exhibits unbounded growth in the vegetation population after a critical value of the Allee parameter. The most significant finding is the observation of a critical Allee parameter beyond which the probability of obtaining extreme events becomes non-zero for all three population densities. Though the emergence of extreme events in the predator population is not affected much by the Allee effect, the prey population shows a sharp increase in the probability of obtaining extreme events after a threshold value of the Allee parameter, and the vegetation population also yields extreme events for sufficiently strong Allee effect. Lastly we consider the influence of additive noise on extreme events. First, we find that noise tames the unbounded vegetation growth induced by Allee effect. More interestingly, we demonstrate that stochasticity drastically diminishes the probability of extreme events in all three populations. In fact for sufficiently high noise, we do not observe any more extreme events in the system. This suggests that noise can mitigate extreme events, and has potentially important bearing on the observability of extreme events in naturally occurring systems.

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“…The search for dynamical systems that yield extreme events, without the drive of external stochastic influences or intrinsic random fluctuations, is a focus of much ongoing research effort from the point of view of basic understanding of complex systems [14][15][16][17] . Additionally, such probabilistic outcomes in dynamical systems are most relevant in the applied context as well, such as in engineering sciences where this direction of research leads to better assessment of risks 18 .…”

Section: Introductionmentioning

confidence: 99%

Enhancement of Extreme Events through the Allee effect and its Mitigation through Noise in a Three Species System

Sen

¹

,

Sinha

²

2021

Preprint

0

View full text Add to dashboard Cite

We consider the dynamics of a three-species system incorporating the Allee Effect, focussing on its influence on the emergence of extreme events in the system. First we find that under Allee effect the regular periodic dynamics changes to chaotic. Further, we find that the system exhibits unbounded growth in the vegetation population after a critical value of the Allee parameter. The most significant finding is the observation of a critical Allee parameter beyond which the probability of obtaining extreme events becomes non-zero for all three population densities. Though the emergence of extreme events in the predator population is not affected much by the Allee effect, the prey population shows a sharp increase in the probability of obtaining extreme events after a threshold value of the Allee parameter, and the vegetation population also yields extreme events for sufficiently strong Allee effect. Lastly we consider the influence of additive noise on extreme events. First, we find that noise tames the unbounded vegetation growth induced by Allee effect. More interestingly, we demonstrate that stochasticity drastically diminishes the probability of extreme events in all three populations. In fact for sufficiently high noise, we do not observe any more extreme events in the system. This suggests that noise can mitigate extreme events, and has potentially important bearing on the observability of extreme events in naturally occurring systems.

show abstract

Dragon-king extreme events as precursors for catastrophic transition

Cited by 29 publications

References 37 publications

Rijke tube: A nonlinear oscillator

Rijke tube: A nonlinear oscillator

Enhancement of extreme events through the Allee effect and its mitigation through noise in a three species system

Enhancement of Extreme Events through the Allee effect and its Mitigation through Noise in a Three Species System

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