Route to extreme events in excitable systems

Karnatak, Rajat; Ansmann, Gerrit; Feudel, Ulrike; Lehnertz, Klaus

doi:10.1103/physreve.90.022917

Cited by 82 publications

(81 citation statements)

References 46 publications

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“…However, chaos is not enough to observe RWs as there are regions of chaotic dynamics with RWs and others without RWs. It is therefore important to understand which are the physical mechanisms that are ultimately responsible for generating extreme fluctuations [17,18].…”

Section: Introductionmentioning

confidence: 99%

Generation of extreme pulses on demand in semiconductor lasers with optical injection

Jin¹,

Chen²,

Masoller³

2017

Opt. Express

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Abstract:The generation of extreme intensity pulses in an optically injected semiconductor laser is studied numerically by using a well-known rate equation model. We show that step-up perturbations of the laser pump current can trigger extreme pulses. We study the perturbation parameters (amplitude, duration) that are more likely to trigger a extreme pulse, and compare the properties of the generated extreme pulses with those spontaneous emitted, which are due to the intrinsic deterministic dynamics of the laser. We study how the phase of the optical field evolves during the pulses and compare both types of pulses (generated by external perturbations and generated by intrinsic nonlinear dynamics). We find that in both cases the phase dynamics is similar with an abrupt rise and fall: as an extreme pulse begins, the phase grows abruptly and reaches a local maximum at the peak of the pulse, then, when the pulse is over, the phase falls down to a value which is similar to the one before the pulse started.

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Section: Introductionmentioning

confidence: 99%

Generation of extreme pulses on demand in semiconductor lasers with optical injection

Jin¹,

Chen²,

Masoller³

2017

Opt. Express

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“…We consider crises in a conceptual climate model [16] as well as in a system of coupled FitzHugh-Nagumo units [17,18]. In both systems, we observe a characteristic scaling behavior to indicate an impending crisis, i.e.…”

mentioning

confidence: 99%

“…Can we predict an interior crisis prior to its occurrence by capitalizing on the scaling behavior? As stated before, crisis-induced intermittency [19] has been recently interpreted with respect to dynamical regimes that allow for the occurrence of extreme events [17,18]. In this context, predicting an interior crisis would mean to predict the transition into a dynamical behavior which exhibits extreme events.…”

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confidence: 99%

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Early warning signal for interior crises in excitable systems

2017

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The ability to reliably predict critical transitions in dynamical systems is a long-standing goal of diverse scientific communities. Previous work focused on early warning signals related to local bifurcations (critical slowing down) and non-bifurcation type transitions. We extend this toolbox and report on a characteristic scaling behavior (critical attractor growth) which is indicative of an impending global bifurcation, an interior crisis in excitable systems. We demonstrate our early warning signal in a conceptual climate model as well as in a model of coupled neurons known to exhibit extreme events. We observed critical attractor growth prior to interior crises of chaotic as well as strange-nonchaotic attractors. These observations promise to extend the classes of transitions that can be predicted via early warning signals.

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“…From this system, time series are obtained which are used in the subsequent sections in order to demonstrate our time series based approach towards the prediction of extreme events. Our system is inspired by models investigated in recent studies of networks of coupled FitzHugh-Nagumo units [21,22]. The FitzHugh-Nagumo unit, also known as Bonhoeffervan der Pol oscillator [23][24][25][26], has two degrees of freedom (a voltage-like variable x and a recovery variable y), can show a variety of dynamics depending on parameter values [27], and can display a characteristic pulse of activity in response to an external stimulus-the hallmark of excitability [28].…”

Section: A Spatially Extended System With Extreme Eventsmentioning

confidence: 99%

Data-driven prediction and prevention of extreme events in a spatially extended excitable system

2015

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Extreme events occur in many spatially extended dynamical systems, often devastatingly affecting human life which makes their reliable prediction and efficient prevention highly desirable. We study the prediction and prevention of extreme events in a spatially extended system, a system of coupled FitzHugh-Nagumo units, in which extreme events occur in a spatially and temporally irregular way. Mimicking typical constraints faced in field studies, we assume not to know the governing equations of motion and to be able to observe only a subset of all phase-space variables for a limited period of time. Based on reconstructing the local dynamics from data and despite being challenged by the rareness of events, we are able to predict extreme events remarkably well. With small, rare, and spatiotemporally localized perturbations which are guided by our predictions, we are able to completely suppress extreme events in this system.

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Route to extreme events in excitable systems

Cited by 82 publications

References 46 publications

Generation of extreme pulses on demand in semiconductor lasers with optical injection

Generation of extreme pulses on demand in semiconductor lasers with optical injection

Early warning signal for interior crises in excitable systems

Data-driven prediction and prevention of extreme events in a spatially extended excitable system

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