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Rate-induced tipping (R-tipping) occurs when a ramp parameter changes rapidly enough to cause the system to tip between co-existing, attracting states, while noise-induced tipping (N-tipping) occurs when there are random transitions between…

Chaotic Dynamics · Physics 2024-10-02 Katherine Slyman , Emmanuel Fleurantin , Christopher K. R. T. Jones

In an ecosystem, environmental changes as a result of natural and human processes can cause some key parameters of the system to change with time. Depending on how fast such a parameter changes, a tipping point can occur. Existing works on…

Populations and Evolution · Quantitative Biology 2023-11-16 Shirin Panahi , Younghae Do , Alan Hastings , Ying-Cheng Lai

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 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…

Dynamical Systems · Mathematics 2013-02-14 Peter Ashwin , Sebastian Wieczorek , Renato Vitolo , Peter Cox

Sudden transitions in the state of a system are often undesirable in natural and human-made systems. Such transitions under fast variation of system parameters are called rate-induced tipping. We experimentally demonstrate rate-induced…

Applied Physics · Physics 2022-09-15 Induja Pavithran , P. R. Midhun , R. I. Sujith

Nonlinear dynamical systems exposed to changing forcing can exhibit catastrophic transitions between alternative and often markedly different states. The phenomenon of critical slowing down (CSD) can be used to anticipate such transitions…

Machine Learning · Computer Science 2024-09-13 Yu Huang , Sebastian Bathiany , Peter Ashwin , Niklas Boers

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

Tipping points (TP) in climate sub-systems are usually thought to occur at a well-defined, critical forcing parameter threshold, via destabilization of the system state by a single, dominant positive feedback. However, coupling to other…

Atmospheric and Oceanic Physics · Physics 2024-12-24 Johannes Lohmann , Henk A. Dijkstra , Markus Jochum , Valerio Lucarini , Peter D. Ditlevsen

Model studies indicate that many climate subsystems, especially ecosystems, may be vulnerable to 'tipping': a 'catastrophic process' in which a system, driven by gradually changing external factors, abruptly transitions (or 'collapses')…

Dynamical Systems · Mathematics 2025-06-30 Dock Staal , Arjen Doelman

An open-source, physics-based tropical cyclone downscaling model is developed, in order to generate a large climatology of tropical cyclones. The model is composed of three primary components: (1) a random seeding process that determines…

Atmospheric and Oceanic Physics · Physics 2023-06-19 Jonathan Lin , Raphael Rousseau-Rizzi , Chia-Ying Lee , Adam Sobel

With rising global temperatures Earth's tipping elements are becoming increasingly more vulnerable to crossing their critical thresholds. The reaching of such tipping points does not only impact other tipping elements through their…

Adaptation and Self-Organizing Systems · Physics 2025-05-08 Tom Bdolach , Jürgen Kurths , Serhiy Yanchuk

Many physical systems are forced by external inputs, which can sometimes take the form of chaotic variation. A particular example is found in applications related to weather and climate, where chaotic variation is prevalent across various…

Chaotic Dynamics · Physics 2026-03-17 Courtney Quinn , Hassan Alkhayuon

The climate system's nonlinear dynamics is influenced by various external forcings and internal feedbacks that can give rise to regional and even global tipping points that may lead to significant and potentially irreversible changes.…

Atmospheric and Oceanic Physics · Physics 2026-01-21 Erik Chavez , Jan Rombouts , Michael Ghil

A dynamical system is said to undergo rate-induced tipping when it fails to track its quasi-equilibrium state due to an above-critical-rate change of system parameters. We study a prototypical model for rate-induced tipping, the saddle-node…

Dynamical Systems · Mathematics 2016-10-12 Paul Ritchie , Jan Sieber

Climate tipping points are critical thresholds in Earth's climate system where a small change can cause abrupt and potentially irreversible shifts towards a new state. Tipping points in the Atlantic Meridional Overturning Circulation (AMOC)…

Atmospheric and Oceanic Physics · Physics 2025-07-10 Jasmine Noory

Tipping points occur in diverse systems in various disciplines such as ecology, climate science, economy or engineering. Tipping points are critical thresholds in system parameters or state variables at which a tiny perturbation can lead to…

We consider the effect on tipping from an additive periodic forcing in a canonical model with a saddle node bifurcation and a slowly varying bifurcation parameter. Here tipping refers to the dramatic change in dynamical behavior…

Classical Analysis and ODEs · Mathematics 2015-08-28 Jielin Zhu , Rachel Kuske , Thomas Erneux

Nonlinear dynamical systems may be exposed to tipping points, critical thresholds at which small changes in the external inputs or in the systems parameters abruptly shift the system to an alternative state with a contrasting dynamical…

Chaotic Dynamics · Physics 2016-10-07 Everton S. Medeiros , Iberê L. Caldas , Murilo S. Baptista , Ulrike Feudel

The theory of alternative stable states and tipping points has garnered substantial attention in the last several decades. It predicts potential critical transitions from one ecosystem state to a completely different state under increasing…

Pattern Formation and Solitons · Physics 2024-09-11 Swarnendu Banerjee , Mara Baudena , Paul Carter , Robbin Bastiaansen , Arjen Doelman , Max Rietkerk

Approaching a dangerous bifurcation, from which a dynamical system such as the Earth's climate will jump (tip) to a different state, the current stable state lies within a shrinking basin of attraction. Persistence of the state becomes…

Dynamical Systems · Mathematics 2015-08-11 Jan Sieber , J. Michael T. Thompson
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