Related papers: Machine learning predictions from unpredictable ch…
As a phenomenon in dynamical systems allowing autonomous switching between stable behaviors, chaotic itinerancy has gained interest in neurorobotics research. In this study, we draw a connection between this phenomenon and the predictive…
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…
Dynamical chaos is a term that encompasses a wide range of nonlinear phenomena such as turbulence, neuronal avalanches, weather patterns, and many others. However, despite much work in the field of chaos, its fundamental physical origin…
Theoretical foundations of chaos have have been predominantly laid out for finite-dimensional dynamical systems, such as the three-body problem in classical mechanics and the Lorenz model in dissipative systems. In contrast, many real-world…
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…
In this paper, we demonstrate, first in literature known to us, that potential functions can be constructed in continuous dissipative chaotic systems and can be used to reveal their dynamical properties. To attain this aim, a Lorenz-like…
A chaotic system is a highly volatile system characterized by its sensitive dependence on initial conditions and outside factors. Chaotic systems are prevalent throughout the world today: in weather patterns, disease outbreaks, and even…
A variety of nonlinear models of biological systems generate complex chaotic behaviors that contrast with biological homeostasis, the observation that many biological systems prove remarkably robust in the face of changing external or…
Different aspects of the predictability problem in dynamical systems are reviewed. The deep relation among Lyapunov exponents, Kolmogorov-Sinai entropy, Shannon entropy and algorithmic complexity is discussed. In particular, we emphasize…
We demonstrate that a deep learning emulator for chaotic systems can forecast phenomena absent from training data. Using the Kuramoto-Sivashinsky and beta-plane turbulence models, we evaluate the emulator through scenarios probing the…
Chaotic iterations have been introduced on the one hand by Chazan, Mi- ranker [6] and Miellou [10] in a numerical analysis context, and on the other hand by Robert [12] and Pellegrin [11] in the discrete dynamical systems frame- work. In…
Forecasting the behavior of high-dimensional dynamical systems using machine learning requires efficient methods to learn the underlying physical model. We demonstrate spatiotemporal chaos prediction using a machine learning architecture…
The presence of physical systems whose characteristics change in a seemingly erratic manner gives rise to the study of chaotic systems. The characteristics of these systems are due to their hypersensitivity to changes in initial conditions.…
In the chaotic quantization approach one replaces the Gaussian white noise of the Parisi-Wu approach of stochastic quantization by a deterministic chaotic process on a very small scale. We consider suitable coupled chaotic noise processes…
Evolutionary game theory has traditionally employed deterministic models to describe population dynamics. These models, due to their inherent nonlinearities, can exhibit deterministic chaos, where population fluctuations follow complex,…
The problem of classifying turbulent environments from partial observation is key for some theoretical and applied fields, from engineering to earth observation and astrophysics, e.g. to precondition searching of optimal control policies in…
Chaotic systems, such as turbulent flows, are ubiquitous in science and engineering. However, their study remains a challenge due to the large range scales, and the strong interaction with other, often not fully understood, physics. As a…
Recent progress toward classifying low-dimensional chaos measured from time series data is described. This classification theory assigns a template to the time series once the time series is embedded in three dimensions. The template…
Time-series forecasting is a challenging problem that traditionally requires specialized models custom-trained for the specific task at hand. Recently, inspired by the success of large language models, foundation models pre-trained on vast…
Chaotic iterations have been introduced on the one hand by Chazan, Miranker [5] and Miellou [9] in a numerical analysis context, and on the other hand by Robert [11] and Pellegrin [10] in the discrete dynamical systems framework. In both…