Related papers: Rate-induced tipping can trigger plankton blooms
A habitat that is moving due to environmental change may result in tipping to extinction if the rate at which it moves is too great. We use a scalar reaction-diffusion equation with a non-autonomous reaction term, representing a spatially…
The population biology model holds a significant position within ecosystems. Introducing stochastic perturbations into the model can more accurately depict real biological processes. In this paper, we primarily investigate the most probable…
The current definition of rate-induced tipping is tied to the idea of a pullback attractor limiting in forward and backward time to a stable quasi-static equilibrium. Here we propose a new definition that encompasses the standard definition…
An in-depth analysis of nonautonomous bifurcations of saddle-node type for scalar differential equations $x'=-x^2+q(t)\,x+p(t)$, where $q\colon\mathbb{R}\to\mathbb{R}$ and $p\colon\mathbb{R}\to\mathbb{R}$ are bounded and uniformly…
The current configuration of the ocean overturning involves upwelling predominantly in the Southern Ocean and sinking predominantly in the Atlantic basin. The reasons for this remain unclear, as both models and paleoclimatic observations…
The ocean is filled with microscopic microalgae called phytoplankton, which together are responsible for as much photosynthesis as all plants on land combined. Our ability to predict their response to the warming ocean relies on…
In ecology, climate and other fields, (sub)systems have been identified that can transition into a qualitatively different state when a critical threshold or tipping point in a driving process is crossed. An understanding of those tipping…
Many turbulent flows undergo drastic and abrupt configuration changes with huge impacts. As a paradigmatic example we study the multistability of jet dynamics in a barotropic beta plane model of atmosphere dynamics. It is considered as the…
Abrupt transitions leading to algal blooms are quite well known in aquatic ecosystems and have important implications for the environment. These ecosystem shifts have been largely attributed to nutrient dynamics and food web interactions.…
Bifurcations can cause dynamical systems with slowly varying parameters to transition to far-away attractors. The terms ``critical transition'' or ``tipping point'' have been used to describe this situation. Critical transitions have been…
It is frequently assumed that in the limit of vanishing cooling rate, the glass transition phenomenon becomes a thermodynamic transition at a temperature $T_{K}$. However, with any finite cooling rate, the system falls out of equilibrium at…
We show quantitatively how the collision rate of droplets of visible moisture in turbulent air increases very abruptly as the intensity of the turbulence passes a threshold, due to the formation of fold caustics in their velocity field. The…
The motility of microorganisms is often biased by gradients in physical and chemical properties of their environment, with myriad implications on their ecology. Here we show that fluid acceleration reorients gyrotactic plankton, triggering…
In multiple time-scale (singularly perturbed) dynamical systems, canards are counterintuitive solutions that evolve along both attracting and repelling invariant manifolds. In two dimensions, canards result in periodic oscillations whose…
We study the mitigation of climate tipping point transitions using an energy balance model. The evolution of the global mean surface temperature is coupled with the CO2 concentration through the green house effect. We model the CO2…
The ocean is filled with phytoplankton that contribute as much photosynthesis as all land plants combined, making them vital to the carbon cycle and climate system. Recent advances in flow cytometry allow oceanographers to measure the…
In nonlinear dynamical systems, tipping refers to a critical transition from one steady state to another, typically catastrophic, steady state, often resulting from a saddle-node bifurcation. Recently, the machine-learning framework of…
Earth system tipping elements have been predominantly investigated for their potential to trigger \textit{negative} ecological, climatic, and societal shifts. Yet, an overlooked but seminal avenue exists in the form of \textit{positive}…
The formation and amplification of streamwise velocity perturbations induced by cross-stream disturbances is ubiquitous in shear flows. This disturbance growth mechanism, so neatly identified by Ellingsen and Palm in 1975, is a key process…
A tilting phase transition is predicted for systems comprising rod like molecules which are irreversibly grafted to a flat surface, so that the non interacting rods are perpendicularly oriented. The transition is controlled by the grafting…