Related papers: Predictability problem in dynamical systems and in…
We introduce a numerically stable reformulation of controllability scoring based on a scaled controllability Gramian, which remains reliably computable even for unstable systems. The resulting optimization problems define dynamics-aware…
We study discrete-time predictable forward processes when trading times do not coincide with performance evaluation times in a binomial tree model for the financial market. The key step in the construction of these processes is to solve a…
We first show that the intrinsic, geometrical structure of a dynamical horizon is unique. A number of physically interesting constraints are then established on the location of trapped and marginally trapped surfaces in the vicinity of any…
A discrete-time version of the replicator equation for two-strategy games is studied. The stationary properties differ from that of continuous time for sufficiently large values of the parameters, where periodic and chaotic behavior replace…
Since the prediction of climate is mainly considered as a prediction of second kind, it is indispensable to assess the accuracy with which these boundary conditions can be determined so that we can find a reasonable answer, whether climate…
Many chemical processes exhibit diverse timescale dynamics with a strong coupling between timescale sensitive variables. Model predictive control with a non-uniformly spaced optimisation horizon is an effective approach to multi-timescale…
We review recent progress in attaining a quantitative understanding of the scarring phenomenon, the non-random behavior of quantum wavefunctions near unstable periodic orbits of a classically chaotic system. The wavepacket dynamics…
We analytically determine the number and distribution of fixed points in a canonical model of a chaotic neural network. This distribution reveals that fixed points and dynamics are confined to separate shells in phase space. Furthermore,…
The Madden-Julian oscillation (MJO) is a planetary-scale, intraseasonal tropical rainfall phenomenon crucial for global weather and climate; however, its dynamics and predictability remain poorly understood. Here, we leverage deep learning…
We scrutinize the use of machine learning, based on reservoir computing, to build data-driven effective models of multiscale chaotic systems. We show that, for a wide scale separation, machine learning generates effective models akin to…
We propose a framework for studying predictability of extreme events in complex systems. Major conceptual elements -- direct cascading or fragmentation, spatial dynamics, and external driving -- are combined in a classical age-dependent…
In principle, all the natural systems such as biological, ecological and economical systems are structure-variable systems (in which some environment parameters are not fixed). In this Letter we show that data sequences from many…
We consider the safety evaluation of discrete time, stochastic systems over a finite horizon. Therefore, we discuss and link probabilistic invariance with reachability as well as reach-avoid problems. We show how to efficiently compute…
Catastrophic transitions, where a system shifts abruptly between alternate steady states, are a generic feature of many nonlinear systems. Recently these regime shift were suggested as the mechanism underlies many ecological catastrophes,…
Chaotic multiscale dynamical systems are common in many areas of science, one of the examples being the interaction of the low-frequency dynamics in the atmosphere with the fast turbulent weather dynamics. One of the key questions about…
Some dynamical properties present in a problem concerning the acceleration of particles in a wave packet are studied. The dynamics of the model is described in terms of a two-dimensional area preserving map. We show that the phase space is…
A multidimensional chaos is generated by a special initial value problem for the non-autonomous impulsive differential equation. The existence of a chaotic attractor is shown, where density of periodic solutions, sensitivity of solutions…
We introduce a new analytical method, which allows to find out chaotic dynamics in non-smooth dynamical systems. A simple mechanical system consisting of a mass and a dry friction element is considered as an example. The corresponding…
This paper is the second in a series of two, and describes the current state of the art in modelling and prediction of chaotic time series. Sampled data from deterministic non-linear systems may look stochastic when analysed with linear…
A novel type of trajectory on semiflows, called asymptotically unpredictable, was proposed by Fen and Tokmak Fen [15]. The presence of sensitivity, which is an indispensable feature of chaotic dynamics, is a crucial property that arises…