Extreme events in dynamical systems and random walkers: A review

Chowdhury, Sayantan Nag; Ray, Arnob; Dana, Syamal K.; Ghosh, Dibakar

doi:10.1016/j.physrep.2022.04.001

Cited by 49 publications

(20 citation statements)

References 335 publications

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“…Finally, the emergence of different dynamical states and regions of EE and NEE are plotted in two-parameter diagrams as a function of the excitation parameters, clearly displaying the emergence of distinct bifurcation routes. The results discussed in this paper are essential for understanding the emergence of EE in nonlinear systems [ 62 ]. We also believe that the results obtained here may be experimentally realizable using analog electronic circuits.…”

Section: Discussionmentioning

confidence: 99%

Route to extreme events in a parametrically driven position-dependent nonlinear oscillator

et al. 2023

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We explore the dynamics of a damped and driven Mathews–Lakshmanan oscillator type model with position-dependent mass term and report two distinct bifurcation routes to the advent of sudden, intermittent large-amplitude chaotic oscillations in the system. We characterize these infrequent and recurrent large oscillations as extreme events (EE) when they are significantly greater than the pre-defined threshold height. In the first bifurcation route, the system exhibits a bifurcation from quasiperiodic (QP) attractor to chaotic attractor via strange non-chaotic (SNA) attractor as a function of damping parameter. In the second route, the chaotic attractor in the form of EE has emerged directly from the QP attractor. Hence, to the best of our knowledge, this is the first study to report the birth of EE from these two distinct bifurcation routes. We also discuss that EE are emerged due to the sudden expansion of the chaotic attractor via interior crisis in the system. Regions of different dynamical states are distinguished using the Lyapunov exponent spectrum. Further, SNA and QP dynamics are determined using the singular spectrum analysis and 0–1 test. The region of EE is characterized using the threshold height.

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Section: Discussionmentioning

confidence: 99%

Route to extreme events in a parametrically driven position-dependent nonlinear oscillator

et al. 2023

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“…A higher significant height h s1 = x max + 6σ (horizontal red dashed line) is defined to gauge the extent of the spike height and present a picture that they even cross this larger significant threshold height. Such occasional large events are often reported as extreme events in the literature 27,29 . The probability density distribution (PDF) of all the local peaks x max = x n shows an interesting distribution that follows a power law against the height of spikes 27,28 .…”

Section: Coupled Hindmarsh-rose Neuron Modelmentioning

confidence: 97%

“…We start our first numerical experiment on the emergence of hyperchaos in a coupled Hindmarsh-Rose neuron model [27][28][29] that is triggered by Pomeau-Manneville intermittency. The coupled neuron model is described as…”

Section: Coupled Hindmarsh-rose Neuron Modelmentioning

confidence: 99%

Transition to hyperchaos: Sudden expansion of attractor and intermittent large-amplitude events in dynamical systems

Kingston

Kapitaniak

Dana

2022

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Hyperchaos is distinguished from chaos by the presence of at least two positive Lyapunov exponents instead of just one in dynamical systems. A general scenario is presented here that shows emergence of hyperchaos with a sudden large expansion of the attractor of continuous dynamical systems at a critical parameter when the temporal dynamics shows intermittent large-amplitude spiking or bursting events. The distribution of local maxima of the temporal dynamics is non-Gaussian with a tail, confirming a rare occurrence of the large-amplitude events. We exemplify our results on the sudden emergence of hyperchaos in three paradigmatic models, namely, a coupled Hindmarsh–Rose model, three coupled Duffing oscillators, and a hyperchaotic model.

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“…The trajectory of the attractors in coupled systems departs from the synchronization manifold to the transverse direction of the manifold. During such a transition, a synchronization error of dynamics can show zero or nonzero and is referred to as on-off intermittency [16].…”

mentioning

confidence: 99%

“…Moreover, previous studies discovered that extreme or rare events can occur as a result of chaotic or stochastic processes [16]. In particular, the appearance of EE has been reported in micro-electromechanical cantilevers with discontinuous boundaries and diode lasers with phase-conjugate feedback [17,18].…”

mentioning

confidence: 99%

Emergence of extreme events in a quasi-periodic oscillator

Premraj¹,

Sathiyadevi²,

Kumarasamy³

et al. 2023

Preprint

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Extreme events are unusual and rare large-amplitude fluctuations that occur can unexpectedly in nonlinear dynamical systems. Events above the extreme event threshold of the probability distribution of a nonlinear process characterize extreme events. Different mechanisms for the generation of extreme events and their prediction measures have been reported in the literature. Based on the properties of extreme events, such as rare in the frequency of occurrence and extreme in amplitude, various studies have shown that extreme events are both linear and nonlinear in nature. Interestingly, in this work, we report on a special class of extreme events which are nonchaotic and nonperiodic. These nonchaotic extreme events appear in between the quasi-periodic and chaotic dynamics of the system. We report the existence of such extreme events with various statistical measures and characterization techniques.

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Extreme events in dynamical systems and random walkers: A review

Cited by 49 publications

References 335 publications

Route to extreme events in a parametrically driven position-dependent nonlinear oscillator

Route to extreme events in a parametrically driven position-dependent nonlinear oscillator

Transition to hyperchaos: Sudden expansion of attractor and intermittent large-amplitude events in dynamical systems

Emergence of extreme events in a quasi-periodic oscillator

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