Related papers: Rare events in a stochastic vegetation-water dynam…
We propose a new procedure to monitor and forecast the onset of transitions in high dimensional complex systems. We describe our procedure by an application to the Tangled Nature model of evolutionary ecology. The quasi-stable…
The analysis of dynamical systems is a fundamental tool in the natural sciences and engineering. It is used to understand the evolution of systems as large as entire galaxies and as small as individual molecules. With predefined conditions…
The mean exit time escaping basin of attraction in the presence of white noise is of practical importance in various scientific fields. In this work, we propose a strategy to control mean exit time of general stochastic dynamical systems to…
We show that a neural network originally designed for language processing can learn the dynamical rules of a stochastic system by observation of a single dynamical trajectory of the system, and can accurately predict its emergent behavior…
Population dynamics in random ecological networks are investigated by analyzing a simple deterministic equation. It is found that a sequence of abrupt changes of populations punctuating quiescent states characterize the long time behavior.…
We introduce a mathematical model of savanna vegetation dynamics. The usual approach of nonequilibrium ecology is extended by including the impact of wet and dry seasons. We present and rigorously analyze a model describing a mixed…
This paper presents a novel data-driven approach for predicting the number of vegetation-related outages that occur in power distribution systems on a monthly basis. In order to develop an approach that is able to successfully fulfill this…
The interplay between stochastic chemical reactions and diffusion can generate rich spatiotemporal patterns. While the timescale for individual reaction or diffusion events may be very fast, the timescales for organization can be much…
This work proposes an innovative approach using machine learning to predict extreme events in time series of chaotic dynamical systems. The research focuses on the time series of the H\'enon map, a two-dimensional model known for its…
We consider potential type dynamical systems in finite dimensions with two meta-stable states. They are subject to two sources of perturbation: a slow external periodic perturbation of period $T$ and a small Gaussian random perturbation of…
In this paper, we consider a stochastic system described by a differential equation admitting a spatially varying random coefficient. The differential equation has been employed to model various static physics systems such as elastic…
Stochastic processes have found numerous applications in science, as they are broadly used to model a variety of natural phenomena. Due to their intrinsic randomness and uncertainty, they are, however, difficult to characterize. Here, we…
We consider a stochastic population model where the intrinsic or demographic noise causes cycling between states before the population eventually goes extinct. A master equation approach coupled with a WKB (Wentzel-Kramers-Brillouin)…
The problem of metastability for a stochastic dynamics with a parallel updating rule is addressed in the Freidlin--Wentzel regime, namely, finite volume, small magnetic field, and small temperature. The model is characterized by the…
We propose a new method for spatio-temporal forecasting on arbitrarily distributed points. Assuming that the observed system follows an unknown partial differential equation, we derive a continuous-time model for the dynamics of the data…
We develop a non-empirical scheme to search for the minimum-energy escape paths from the minima of the potential surface to unknown saddle points nearby. A stochastic algorithm is constructed to move the walkers up the surface through the…
Extreme events occur across the natural, engineering, and socioeconomic sciences, where rare but high-impact episodes can lead to disproportionate consequences that pose major challenges for prediction and risk management. Existing studies…
The scarcity of water characterising drylands forces vegetation to adopt appropriate survival strategies. Some of these generate water-vegetation feedback mechanisms that can lead to spatial self-organisation of vegetation, as it has been…
This article reviews the concepts and methods of variational path sampling. These methods allow computational studies of rare events in systems driven arbitrarily far from equilibrium. Based upon a statistical mechanics of trajectory space…
We investigate fluid transport in random velocity fields with unsteady drift. First, we propose to quantify fluid transport between flow regimes of different characteristic motion, by escape probability and mean residence time. We then…