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Related papers: A rate-induced tipping in the Pearson diffusion

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Tipping refers to the transition of a system from one state to another. In this study, we focus on shock-induced tipping, which occurs due to a sudden and large disturbance in a control parameter, which is referred to as the shock. This…

Fluid Dynamics · Physics 2026-03-17 Bhadra Sreelatha , Rohit Radhakrishnan , R. I. Sujith

A classical scenario for tipping is that a dynamical system experiences a slow parameter drift across a fold tipping point, caused by a run-away positive feedback loop. We study what happens if one turns around after one has crossed the…

Dynamical Systems · Mathematics 2019-01-21 Paul Ritchie , Ozkan Karabacak , Jan Sieber

Tipping in multistable systems occurs usually by varying the input slightly, resulting in the output switching to an often unsatisfactory state. This phenomenon is manifested in thermoacoustic systems. This thermoacoustic instability may…

Adaptation and Self-Organizing Systems · Physics 2020-09-29 Xiaoyu Zhang , Yong Xu , Qi Liu , Jürgen Kurths , Celso Grebogi

This study explores the connection between disinformation, defined as deliberate spread of false information, and rate-induced tipping (R-tipping), a phenomenon where systems undergo sudden changes due to rapid shifts in ex-ternal forces.…

Dynamical Systems · Mathematics 2024-01-23 Arindam Kumar Paul , M. Haider Ali Biswas

Tipping points characterize situations where a regulated system may experience a sudden and irreversible change and are generally associated with a random state of the system below which the change materializes. In this paper, we study a…

Optimization and Control · Mathematics 2026-02-25 Jean-Paul Décamps , Fabien Gensbittel , Thomas Mariotti , Stéphane Villeneuve

We present a novel exactly solvable ordinary differential equation model for rate-induced tipping: a dynamic phenomenon of dynamical systems where a time-dependent parameter triggers the transition of stability of a system. Our model…

Dynamical Systems · Mathematics 2026-03-10 Hidekazu Yoshioka

Tipping points have been shown to be ubiquitous, both in models and empirically in a range of physical and biological systems. The question of how tipping points cascade through systems has been less well studied and is an important one. A…

Dynamical Systems · Mathematics 2020-11-19 Abhishek Mallela , Alan Hastings

Tipping points are one of the hot topics in modern physics of complex systems. But what is a tipping point? A generic definition declares it as ``a state of the system where a small change in its parameters can lead to a significant change…

Populations and Evolution · Quantitative Biology 2026-02-25 Alan Hastings , Sergei Petrovskii , Valerio Lucarini , Andrew Morozov

In this paper we consider a diffusion process obtained as a small random perturbation of a dynamical system attracted to a stable equilibrium point. The drift and the diffusive perturbation are assumed to evolve slowly in time. We describe…

Probability · Mathematics 2016-10-23 Mark Freidlin , Leonid Koralov

External and internal factors may cause a system's parameter to vary with time before it stabilizes. This drift induces a regime shift when the parameter crosses a bifurcation. Here, we study the case of an infinite dimensional system: a…

Chaotic Dynamics · Physics 2020-10-14 Julia Cantisán , Jesús M. Seoane , Miguel A. F. Sanjuán

Nonlinear dynamical systems subjected to a combination of noise and time-varying forcing can exhibit sudden changes, critical transitions or tipping points where large or rapid dynamic effects arise from changes in a parameter that are…

Chaotic Dynamics · Physics 2024-05-21 Peter Ashwin , Julian Newman , Raphael Römer

Turing instabilities of reaction-diffusion systems can only arise if the diffusivities of the chemical species are sufficiently different. This threshold is unphysical in most systems with $N=2$ diffusing species, forcing experimental…

Soft Condensed Matter · Physics 2026-03-17 Pierre A. Haas , Raymond E. Goldstein

We consider processes that coincide with a given diffusion process outside a finite collection of domains. In each of the domains, there is, additionally, a large drift directed towards the interior of the domain. We describe the limiting…

Probability · Mathematics 2015-10-20 Mark Freidlin , Leonid Koralov , Alexander Wentzell

It is often known, from modelling studies, that a certain mode of climate tipping (of the oceanic thermohaline circulation, for example) is governed by an underlying fold bifurcation. For such a case we present a scheme of analysis that…

Dynamical Systems · Mathematics 2010-12-15 J. M. T. Thompson , Jan Sieber

The study of pattern emergence together with exploration of the exemplar Turing model is enjoying a renaissance both from theoretical and experimental perspective. Here, we implement a stability analysis of spatially dependent reaction…

Pattern Formation and Solitons · Physics 2019-11-06 Michal Kozák , Eamonn A Gaffney , Václav Klika

We analyze diffusion-driven (Turing) instability of a reaction-diffusion system. The innovation is that we replace the traditional Laplacian diffusion operator with a combination of the fourth order bi-Laplacian operator and the second…

Spectral Theory · Mathematics 2018-07-04 Jooyeon Chung

We study rate-induced phase-tipping (RP-tipping) between two stable limit cycles of a birhythmic oscillator. We say that such an oscillator RP-tips when a time variation of an input parameter preserves the bistability of the limit cycles…

Dynamical Systems · Mathematics 2025-02-14 Ravi Kumar K , Hassan Alkhayuon , Sebastian Wieczorek , Partha Sharathi Dutta

Turing (or double-diffusive) instabilities describe pattern formation in reaction-diffusion systems, and were proposed in 1952 as a potential mechanism behind pattern formation in nature, such as leopard spots and zebra stripes. Because the…

Materials Science · Physics 2020-04-29 M. W. Noble , M. R. Tonks , S. P. Fitzgerald

Analytically tracking patterns emerging from a small amplitude Turing instability to large amplitude remains a challenge as no general theory exists. In this paper, we consider a three component reaction-diffusion system with one of its…

Dynamical Systems · Mathematics 2023-11-06 Christopher Brown , Gianne Derks , Peter van Heijster , David J. B. Lloyd

The properties of the fluctuations large enough to induce bifurcations at open chemical systems at steady constraints are studied. The fluctuations that come from the diffusion-induced noise are considered. It is a generic for the surface…

Statistical Mechanics · Physics 2007-05-23 Maria K. Koleva , L. A. Petrov