Related papers: How Can We Observe and Describe Chaos?
Dynamical systems on the interval were widely studied because they are among the simplest systems and nevertheless they turn out to have complex dynamics. Many works on chaos were inspired by the behaviour of interval maps. However these…
We revisit the global dynamics of unified dark matter cosmological models and analyze it in a new dynamical system setting. In particular, by defining a suitable set of variables we obtain a bounded variable space, a feature that allows a…
The study of the phase space of multidimensional systems is one of the central open problems in dynamical systems. Being able to distinguish chaoticity from regularity in nonlinear dynamical systems, as well as to determine the subspace of…
The scope of this teaching package is to make a brief introduction to some notions and properties of chaotic systems. We first make a brief introduction to chaos in general and then we show some important properties of chaotic systems using…
Chaotic cryptography describes the use of chaos theory (in particular physical dynamical systems working in chaotic regime as part of communication techniques and computation algorithms) to perform different cryptographic tasks in a…
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…
We investigate measures of chaos in the measurement record of a quantum system which is being observed. Such measures are attractive because they can be directly connected to experiment. Two measures of chaos in the measurement record are…
Using a new time-dependent measure, we demonstrate for the first time that each defect in a representative defect-mediated spatiotemporally chaotic system is associated with one to two degrees of dynamical freedom. Furthermore, we show that…
In this paper we present an approach in which synchronization of chaos is used to address identification problems. In particular, we are able to identify: (i) the discontinuity points of systems described by piecewise dynamical equations…
We investigate the structure of the invariant measure of space-time chaos by adopting an "open-system" point of view. We consider large but finite windows of formally infinite one-dimensional lattices and quantify the effect of the…
Quantum chaos is presented as a paradigm of information processing by dynamical systems at the bottom of the range of phase-space scales. Starting with a brief review of classical chaos as entropy flow from micro- to macro-scales, I argue…
I shall briefly survey the current status on more rigorous studies of chaos in fluids by focusing along the line of chaos phenotypes: sensitive dependence on initial data, and recurrence.
in the last decade, studies of chaotic system are more often used for classical choatic system than for quantum chaotic system, there are many ways of observing the chaotic system such us analyzing the frequency with Fourier transform or…
A type of chaos called laminar chaos was found in singularly perturbed dynamical systems with periodically [Phys. Rev. Lett. 120, 084102 (2018)] and quasiperiodically [Phys. Rev. E 107, 014205 (2023)] time-varying delay. Compared to…
This talk summarises what is currently understood about the phenomenon that has come to be known as {\it chaotic mixing}. The first part presents a concise statement as to what chaotic mixing actually is, and then explains why it should be…
Chaos presents complex dynamics arising from nonlinearity and a sensitivity to initial states. These characteristics suggest a depth of expressivity that underscores their potential for advanced computational applications. However,…
The relevance of chaos to evolution is discussed in the context of the origin and maintenance of diversity and complexity. Evolution to the edge of chaos is demonstrated in an imitation game. As an origin of diversity, dynamic clustering of…
This paper studies how complicated and irregular behavior, known as chaos, can arise in a simple mathematical model that includes time delays. The model is a delay differential equation in which the present rate of change depends not only…
The study of chaos has long relied on computationally intensive methods to quantify unpredictability and design control strategies. Recent advances in machine learning, from convolutional neural networks to transformer architectures,…
When implemented in the digital domain with time, space and value discretized in the binary form, many good dynamical properties of chaotic systems in continuous domain may be degraded or even diminish. To measure the dynamic complexity of…