Extreme Events: Mechanisms and Prediction

Farazmand, Mohammad; Sapsis, Themistoklis P.

doi:10.1115/1.4042065

Cited by 104 publications

(64 citation statements)

References 194 publications

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“…The system is multistable if, in the absence of noise, there are several stable fixed points. Much attention has been paid to real-time prediction [14][15][16][17][18] and quantification [19][20][21] of transitions in system (1). Real-time prediction refers to early warning signs of the upcoming transitions that enable their predictions.…”

Section: Introductionmentioning

confidence: 99%

Mitigation of tipping point transitions by time-delay feedback control

Farazmand

2020

Chaos: An Interdisciplinary Journal of Nonlinear Science

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In stochastic multistable systems driven by the gradient of a potential, transitions between equilibria is possible because of noise. We study the ability of linear delay feedback control to mitigate these transitions, ensuring that the system stays near a desirable equilibrium. For small delays, we show that the control term has two effects: i) a stabilizing effect by deepening the potential well around the desirable equilibrium, and ii) a destabilizing effect by intensifying the noise by a factor of (1 − τ α) −1/2 , where τ and α denote the delay and the control gain, respectively. As a result, successful mitigation depends on the competition between these two factors. We also derive analytical results that elucidate the choice of the appropriate control gain and delay that ensure successful mitigations. These results eliminate the need for any Monte Carlo simulations of the stochastic differential equations, and therefore significantly reduce the computational cost of determining the suitable control parameters. We demonstrate the application of our results on two examples.Many complex systems, such as the climate, stock markets, population of species, and the nervous system, have multiple stable equilibrium states. Near the tipping point of the system, small amounts of stochastic disturbances can lead to transitions between these equilibria. Typically, one of the equilibria is desirable and transitions away from it lead to catastrophic consequences. Here, we analyze the ability of a delay feedback control to mitigate transitions away from a desirable equilibrium. arXiv:1911.05292v2 [math.OC]

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Section: Introductionmentioning

confidence: 99%

Mitigation of tipping point transitions by time-delay feedback control

Farazmand

2020

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…The extreme value threshold E e (respectively, Z e ) are set as the mean of energy (respectively, dissipation) plus one standard deviation. Figure 14 also shows the corresponding P ee computed from equation (17). The extreme event threshold according to the indicator λ is the point at which P ee (λ e ) = 0.5.…”

Section: Prediction Resultsmentioning

confidence: 99%

“…First row shows the conditional PDF pZ |λ and the second row shows the corresponding probability of future extreme events defined in Eq. (17).…”

Section: Prediction Resultsmentioning

confidence: 99%

“…Many aspects of these intermittent bursts remain elusive primarily because of the intrinsic high dimensionality of the underlying turbulent attractor that limits the applicability of existing mathematical approaches [14,17]. In particular, extreme events due to their rare character cannot be 'seen' effectively by energy-based methods, such as Proper Orthogonal Decomposition (POD).…”

Section: Introductionmentioning

confidence: 99%

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Are extreme dissipation events predictable in turbulent fluid flows?

2019

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We derive precursors of extreme dissipation events in a turbulent channel flow. Using a recently developed method that combines dynamics and statistics for the underlying attractor, we extract a characteristic state that precedes laminarization events that subsequently lead to extreme dissipation episodes. Our approach utilizes coarse statistical information for the turbulent attractor, in the form of second order statistics, to identify high-likelihood regions in the state space. We then search within this high probability manifold for the state that leads to the most finite-time growth of the flow kinetic energy. This state has both high probability of occurrence and leads to extreme values of dissipation. We use the alignment between a given turbulent state and this critical state as a precursor for extreme events and demonstrate its favorable properties for prediction of extreme dissipation events. Finally, we analyze the physical relevance of the derived precursor and show its robust character for different Reynolds numbers. Overall, we find that our choice of precursor works well at the Reynolds number it is computed at and at higher Reynolds number flows with similar extreme events.

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“…The agents are allowed to interact with each other only when they move into the same coupling zone. The study of extreme events [71] have received less attention, although discovery of definitive extreme events indicating threshold is highly desirable for its scientific understanding, particularly for the problems, such as earthquakes, epileptic seizures and social dynamics, where the governing equations are unknown. Extreme events on complex networks play an important role due to its wide possible applications on dynamical processes.…”

Section: Discussionmentioning

confidence: 99%

Synchronization to extreme events in moving agents

et al. 2019

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Interactions amongst agents frequently exist only at particular moments in time, depending on their closeness in space and movement parameters. Here we propose a minimal model of moving agents where the network of contacts changes over time due to their motion. In particular, agents interact based on their proximity in a two-dimensional space, but only if they belong to the same fixed interaction zones. Our research reveals the emergence of global synchronization if all the interaction zones are attractive. However, if some of the interaction zones are repulsive, they deflect synchrony and lead to short-lasting but recurrent deviations that constitute extreme events in the network. We use two paradigmatic oscillators for the description of the agent dynamics to demonstrate our findings numerically, and we also provide an analytical formulation to describe the emergence of complete synchrony and the thresholds that distinguish extreme events from other intermittent states based on the peak-over-threshold approach. IntroductionResearch to understand the interplay between complex networks and the dynamical properties of coupled oscillators has been a hotspot for the last few decades and the developing phenomenon of synchronization [1-4] is one of the most important dynamical processes that has been in the center of these researches. Cooperation [5,6] and time series analysis [7,8] in complex network have been studied in the past few years. From the perspective of synchronization among coupled oscillators placed into a complex network [9,10], the correlation between the network's topology and local dynamics is quite decisive. Here, synchronization signifies a process of adaptation to a common collective behavior of oscillators due to their interaction. In most of the previous studies of such systems, the network topology is assumed to be invariant over time and thus the system is controlled by a deterministic static formation for all the course of time. But such a crude assumption regarding the network connectivity inhibits one to model and study most of the practical instances.Recently, time-varying networks have grabbed the attention of the researchers due to their enormous applications in various fields like functional brain network [11], epidemic modeling [12], communication systems [13,14] and many more. Time-varying networks, also known as temporal networks [15] indicate those networks in which links get activated for a certain course of time. On the assumption of time-invariant nodes which are static over time, many network architecture is studied, e.g. power transmission elements are considered as such nodes among which haphazard links are treated as the coupling between elements of the power transmission system [16]. Even for functional brain networks [11], these types of nodes are considered to characterize the dynamical evolution. Particularly, the scenario of time-varying networks owing to the mobility in the nodes is really a significant platform to study several dynamical processes over them in which no...

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Extreme Events: Mechanisms and Prediction

Cited by 104 publications

References 194 publications

Mitigation of tipping point transitions by time-delay feedback control

Mitigation of tipping point transitions by time-delay feedback control

Are extreme dissipation events predictable in turbulent fluid flows?

Synchronization to extreme events in moving agents

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