Related papers: What do we mean, 'tipping cascade'?
The realization that complex systems such as ecological communities can collapse or shift regimes suddenly and without rapid external forcing poses a serious challenge to our understanding and management of the natural world. The potential…
These lecture notes describe a basic theory of chemically active droplets, which are droplets kept away from equilibrium by driven chemical reactions. The notes assume a basic familiarity with equilibrium thermodynamics of phase separation,…
Turing patterns are a central paradigm for describing spatial patterns in nature. The corresponding theory of reaction-diffusion dynamics combines ideal diffusion with nonlinear reactions, resulting in patterns when species diffuse at…
Network structures in a wide array of systems such as social networks, transportation, power and water distribution infrastructures, and biological and ecological systems can exhibit critical thresholds or tipping points beyond which there…
Oscillations are observed in all branches of science and culture, ranging from the behavior of ele-mentary particles, atoms, molecules in simple chemical or physical systems or even in complex organisms, up to oscillations of the behavior…
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…
We investigate how nonlinear behaviour (both of forcing in time and of the system itself) can affect the skill of early warning signals to predict tipping in (directionally) coupled bistable systems when using measures based on critical…
The possible dynamics of an ecosystem with three interconnected patches among which one population can migrate are investigated, paying attention to the consequences that possible disruption in the communicating paths can cause.
Phase transitions are emergent phenomena where microscopic interactions drive a disordered system into a collectively ordered phase. Near the boundary between two phases, the system can exhibit critical, scale-invariant behavior. Here, we…
The Amazon rainforest and the AMOC are considered to be tipping elements: they are important components of the Earth system, but may collapse under climate change. Moreover, an AMOC collapse may favor the transition of the rainforest to a…
Phase separation is the thermodynamic process that explains how droplets form in multicomponent fluids. These droplets can provide controlled compartments to localize chemical reactions, and reactions can also affect the droplets' dynamics.…
The central problem of fully developed turbulence is the energy cascading process. It has revisited all attempts at a full physical understanding or mathematical formulation. The main reason for this failure are related to the large…
Ecological communities with many species can be classified into dynamical phases. In systems with all-to-all interactions, a phase where a fixed point is always reached and a dynamically-fluctuating phase have been found. The dynamics when…
It is well known that the addition of noise to a multistable dynamical system can induce random transitions from one stable state to another. For low noise, the times between transitions have an exponential tail and Kramers' formula gives…
The outbreak of epidemics, the emergence of the financial crisis, the collapse of ecosystem, and the explosive spreading of rumors, we face many challenges in today's world. These real-world problems can be abstracted into a sequential…
In network systems, a local perturbation can amplify as it propagates, potentially leading to a large-scale cascading failure. Here we derive a continuous model to advance our understanding of cascading failures in power-grid networks. The…
One of the most prominent climate tipping elements is the Atlantic Meridional Overturning Circulation (AMOC), which can potentially collapse due to the input of fresh water in the North Atlantic. Although AMOC collapses have been induced in…
The Atlantic Meridional Overturning Circulation (AMOC) is a key component of the climate system and considered to be a tipping element. There is still a large uncertainty on the critical global warming level at which the AMOC will start to…
Prediction of climate tipping is challenging due to the lack of recent observation of actual climate tipping. Despite many previous efforts to accurately predict the existence and timing of climate tippings under specific climate scenarios,…
An important challenge in several disciplines is to understand how sudden changes can propagate among coupled systems. Examples include the synchronization of business cycles, population collapse in patchy ecosystems, markets shifting to a…