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Chaos and oscillations continue to capture the interest of both the scientific and public domains. Yet despite the importance of these qualitative features, most attempts at constructing mathematical models of such phenomena have taken an…

Modern machine learning methods including deep learning have achieved great success in predictive accuracy for supervised learning tasks, but may still fall short in giving useful estimates of their predictive {\em uncertainty}. Quantifying…

Machine learning processes, e.g. ''learning in games'', can be viewed as non-linear dynamical systems. In general, such systems exhibit a wide spectrum of behaviors, ranging from stability/recurrence to the undesirable phenomena of chaos…

Representing and quantifying uncertainty in physical parameterisations is a central challenge in weather and climate modelling, and approaches are often developed separately for different timescales. Here, we introduce a unified framework…

In many situations, the statistical properties of wave systems with chaotic classical limits are well-described by random matrix theory. However, applications of random matrix theory to scattering problems require introduction of system…

The recent framework of performative prediction is aimed at capturing settings where predictions influence the target/outcome they want to predict. In this paper, we introduce a natural multi-agent version of this framework, where multiple…

We consider the problems of chaos in disorder and temperature for coupled copies of the mixed p-spin models. Under certain assumptions on the parameters of the models we will first prove a weak form of chaos by showing that the overlap is…

For most statistical postprocessing schemes used to correct weather forecasts, changes to the forecast model induce a considerable reforecasting effort. We present a new approach based on response theory to cope with slight model changes.…

The destruction of a chaotic attractor leading to rough changes in the dynamics of a dynamical system is studied. Local bifurcations are characterised by a single or a pair of characteristic exponents crossing the imaginary axis. The…

The dynamics of the tubular chemical reactor with mass recycle were examined. In such a system, temperature and concentrations may oscillate chaotically. This means that state variable values are then unpredictable. In this paper it has…

Encouraged by decision makers' appetite for future information on topics ranging from elections to pandemics, and enabled by the explosion of data and computational methods, model based forecasts have garnered increasing influence on a…

This article is talking about the study constructive method of structural identification systems with chaotic dynamics. It is shown that the reconstructed attractors are a source of information not only about the dynamics but also on the…

Turbulent dynamical systems characterized by both a high-dimensional phase space and a large number of instabilities are ubiquitous among many complex systems in science and engineering. The existence of a strange attractor in the turbulent…

When a medium composed of microscopic elements is subjected to a high intensity field, the individual behaviors of microscopic elements can become chaotic. In such cases it is important to consider the effects of this irregularity at…

The large scale fluctuations of the ordered state in active matter systems are usually characterised by studying the "giant number fluctuations" of particles in any finite volume, as compared to the expectations from the central limit…

In this paper, we present a unified framework of multiple attractors including multistability, multiperiodicity and multichaos. Multichaos, which means that the chaotic solution of a system lies in different disjoint invariant sets with…

We use physical principles to derive a water wheel model under the assumption of an asymmetric water wheel for which the water inflow rate is in general unsteady (modeled by an arbitrary function of time). Our model allows one to recover…

Model uncertainty is a crucial issue in statistics, econometrics and machine learning, yet its definition remains ambiguous and is subject to various interpretations in the literature. So far, there has not been a universally accepted…

We consider a many-parametric piecewise mapping with discontinuity. That is a one dimensional model of singular dynamic system. The stability boundary are calculated analytically and numerically. New typical features of stable cycle…

It is frequently asserted that in a chaotic system two initially close points will separate at an exponential rate governed by the largest global Lyapunov exponent. Local Lyapunov exponents, however, are more directly relevant to…