Sebastian Wieczorek

University College Cork

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Bernd Krauskopf

University of Auckland

D. Lenstra

Eindhoven University of Technology

Weng W. Chow

Sandia National Laboratories

Hassan Alkhayuon

University College Cork

Peter M. Cox

University of Exeter

Peter Ashwin

University of Exeter

H. Erzgräber

University of Exeter

Kieran F. Mulchrone

University College Cork

AŞ

Alin Ştefănescu

University of Bucharest

Rebecca C. Tyson

Okanagan University College

Cooperative Institutions

University College Cork

University of Exeter

Sandia National Laboratories California

National University of Ireland

Sandia National Laboratories

Technische Universität Berlin

Office of Scientific and Technical Information

National Technical Information Service

Vrije Universiteit Amsterdam

Vrije Universiteit Brussel

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Accumulating regions of winding periodic orbits in optically driven lasers

Physica D Nonlinear Phenomena (2002)

Bernd Krauskopf Sebastian Wieczorek

Saddle

10.1016/s0167-2789(02)00650-4

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Citations (39)

When to Expect Rate-Induced Tipping in Natural and Human Systems

Paul Ritchie Hassan Alkhayuon Peter M. Cox Sebastian Wieczorek

Over the last two decades, tipping points have become a hot topic due to the devastating consequences that they may have on natural and human systems. Tipping points are typically associated with a system bifurcation when external forcing crosses a critical level, causing an abrupt transition to an alternative, and often less desirable, state. However, the rate of change in forcing is arguably of even greater relevance in the human-dominated anthropocene, but is rarely examined as a potential sole mechanism for tipping points. Thus, I will introduce the related phenomenon of rate-induced tipping: an instability that occurs when external forcing varies across some critical rate, usually without crossing any bifurcations. First, I will explain when to expect rate-induced tipping. Then, using illustrating examples of differing complexity I will highlight universal and generic properties of rate-induced tipping in a range of natural and human systems.

Forcing (mathematics)

Tipping point (physics)

Relevance

10.5194/egusphere-egu23-8105

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Citations (1)

Synchronisation vs. resonance: Isolated resonances in damped nonlinear oscillators

Physica D Nonlinear Phenomena (2018)

Arianna Marchionne Peter Ditlevsen Sebastian Wieczorek

Multistability

Forcing (mathematics)

Duffing equation

Numerical continuation

Nonlinear resonance

10.1016/j.physd.2018.05.004

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Citations (20)

Strong coupling theory of synchronization in coupled-cavity lasers

Frontiers in Optics (2003)

Sebastian Wieczorek Weng W. Chow

The goal of this study is to understand synchronization and chaotic dynamics of coupled-cavity lasers under all coupling conditions. To achieve this, a strong-coupling model, which describes the temporal evolution of the laser variables as well as the spatial mode structure, is subject to bifurcation analysis.

Optical chaos

Coupled mode theory

Mode coupling

10.1364/fio.2003.thf4

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Citations (0)

40 GHz Bandwidth and 64 GHz Resonance Frequency in Injection-Locked 1.55 $\mu$m VCSELs

IEEE Journal of Selected Topics in Quantum Electronics (2007)

Lukas Chrostowski Behnam Faraji Werner Hofmann Markus‐Christian Amann Sebastian Wieczorek

Injection locking is shown to greatly enhance the resonance frequency of 1.55 mum vertical-cavity surface-emitting lasers (VCSELs), from 10 to 60 GHz, under ultrahigh injection locking conditions. Using injection locking to increase the laser resonance frequency, together with a low parasitic VCSEL design, a 3 dB bandwidth of over 40 GHz was attained, a record broadband performance for directly modulated VCSELs. VCSELs with slightly detuned polarization modes are injection locked with controlled polarization angles. For the first time, a dual-resonance frequency response is observed, and is explained with a two polarization-mode injection-locked rate equation model.

Injection locking

Vertical-cavity surface-emitting laser

Mode-Locking

10.1109/jstqe.2007.904417

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Citations (77)

Comment on egusphere-2022-1176

Paul Ritchie Hassan Alkhayuon Peter M. Cox Sebastian Wieczorek

Abstract. Over the last two decades, tipping points have become a hot topic due to the devastating consequences that they may have on natural and human systems. Tipping points are typically associated with a system bifurcation when external forcing crosses a critical level, causing an abrupt transition to an alternative, and often less desirable, state. The main message of this review is that the rate of change in forcing is arguably of even greater relevance in the human-dominated anthropocene, but is rarely examined as a potential sole mechanism for tipping points. Thus, we address the related phenomenon of rate-induced tipping: an instability that occurs when external forcing varies across some critical rate, usually without crossing any bifurcations. First, we explain when to expect rate-induced tipping. Then, we use three illustrating examples of differing complexity to highlight universal and generic properties of rate-induced tipping in a range of natural and human systems.

Forcing (mathematics)

Tipping point (physics)

Relevance

10.5194/egusphere-2022-1176-cc1

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Citations (0)

When very slow is too fast - collapse of a predator-prey system

Journal of Theoretical Biology (2019)

Anna Vanselow Sebastian Wieczorek Ulrike Feudel

Alternative stable state

Environmental change

Regime shift

10.1016/j.jtbi.2019.07.008

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Citations (84)

Sudden chaotic transitions in an optically injected semiconductor laser

Optics Letters (2001)

Sebastian Wieczorek Bernd Krauskopf D. Lenstra

We study sudden changes in the chaotic output of an optically injected semiconductor laser. For what is believed to be the first time in this system, we identify bifurcations that cause abrupt changes between different chaotic outputs, or even sudden jumps between chaotic and periodic output. These sudden chaotic transitions involve attractors that exist for large regions in parameter space.

10.1364/ol.26.000816

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Citations (19)

Tipping points in open systems: bifurcation, noise-induced and rate-dependent examples in the climate system

Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences (2012)

Peter Ashwin Sebastian Wieczorek Renato Vitolo Peter M. Cox

Tipping points associated with bifurcations (B-tipping) or induced by noise (N-tipping) are recognized mechanisms that may potentially lead to sudden climate change. We focus here a novel class of tipping points, where a sufficiently rapid change to an input or parameter of a system may cause the system to "tip" or move away from a branch of attractors. Such rate-dependent tipping, or R-tipping, need not be associated with either bifurcations or noise. We present an example of all three types of tipping in a simple global energy balance model of the climate system, illustrating the possibility of dangerous rates of change even in the absence of noise and of bifurcations in the underlying quasi-static system.

Tipping point (physics)

Climate system

10.1098/rsta.2011.0306

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Citations (559)

Noise synchronisation and stochastic bifurcations in lasers

arXiv (Cornell University) (2011)

Sebastian Wieczorek

This paper studies noise synchronisation in terms of random pullback attractors and their instabilities. We consider an ensemble of uncoupled lasers, each being a limit-cycle oscillator, which are driven by the same external white Gaussian noise. As the external-noise strength increases, there is an onset of synchronization and then subsequent loss of synchrony. Local analysis of the laser equations shows that synchronization becomes unstable via stochastic bifurcation to a random strange attractor. The locus of this bifurcation is calculated in the three-dimensional parameter space defined by the Hopf parameter, amount of amplitude-phase coupling or shear, and external-noise strength. The analysis uncovers a square-root law for this stochastic bifurcation.

10.48550/arxiv.1104.4052

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Citations (2)