Related papers: Anticipating tipping in spatiotemporal systems wit…
The early prediction of tipping points, distinguished by sudden and catastrophic shifts from stable states, poses a challenging task that would enable us to assess the impending threat across natural and engineered systems. This threat…
The potential for complex systems to exhibit tipping points in which an equilibrium state undergoes a sudden and often irreversible shift is well established, but prediction of these events using standard forecast modeling techniques is…
Models of complex dynamical systems like the Earth's climate often involve large numbers of uncertain parameters. Comprehensive exploration of the parameter space is typically prohibitive due to excessive computational costs. Systematic…
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…
Reservoir computing has emerged as a powerful framework for time series modelling and forecasting including the prediction of discontinuous transitions. However, the mechanism behind its success is not yet fully understood. This letter…
We study the behaviour at tipping points close to (smoothed) non-smooth fold bifurcations in one-dimensional oscillatory forced systems. The focus is the Stommel-Box, and related climate models, which are piecewise-smooth continuous…
Deducing the states of spatiotemporally chaotic systems (SCSs) as they evolve in time is crucial for various applications. However, it is a dramatic challenge for generally achieving so due to the complexity of non-periodic dynamics and the…
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,…
Tipping behavior can occur when an equilibrium of a dynamical system loses stability in response to a slowly varying parameter crossing a bifurcation threshold, or where noise drives a system from one attractor to another, or some…
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…
We consider the commonly encountered situation (e.g., in weather forecasting) where the goal is to predict the time evolution of a large, spatiotemporally chaotic dynamical system when we have access to both time series data of previous…
Reservoir computing is a novel machine learning algorithm that uses a nonlinear dynamical system to efficiently learn complex temporal patterns from data. The objective of this thesis is to investigate the principles of reservoir computing…
We discuss tipping phenomena (critical transitions) in nonautonomous systems using an example of a bistable ecosystem model with environmental changes represented by time-varying parameters [Scheffer et al., Ecosystems, 11 (2008), pp.…
Complex and nonlinear dynamical systems often involve parameters that change with time, accurate tracking of which is essential to tasks such as state estimation, prediction, and control. Existing machine-learning methods require full state…
The prediction of time series is a challenging task relevant in such diverse applications as analyzing financial data, forecasting flow dynamics or understanding biological processes. Especially chaotic time series that depend on a long…
Machine learning has become a fundamental approach for modeling, prediction, and control, enabling systems to learn from data and perform complex tasks. Reservoir computing is a machine learning tool that leverages high-dimensional…
Reduced-order dynamical models play a central role in developing our understanding of predictability of climate irrespective of whether we are dealing with the actual climate system or surrogate climate-models. In this context, the…
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…
The future behavioural fate of a forced nonlinear system can depend sensitively on the forcing profile as well as natural fluctuations within the system. This is especially the case for rate-induced tipping, where the forcing pushes the…
Recent work has highlighted the utility of methods for early warning signal detection in dynamic systems approaching critical tipping thresholds. Often these tipping points resemble local bifurcations, whose low dimensional dynamics can…