Related papers: How Can We Observe and Describe Chaos?
Chaos is usually referred to the sensitivity to initial conditions in which the nonlinearity plays a crucial role. Beyond such a mathematical description, the understanding of the underlying physical origin of the chaos is still not very…
We show that the output of systems with time-varying delay can exhibit a new kind of chaotic behavior characterized by laminar phases, which are periodically interrupted by irregular bursts. Within each laminar phase the output intensity…
Chaotic dynamics can be quite heterogeneous in the sense that in some regions the dynamics are unstable in more directions than in other regions. When trajectories wander between these regions, the dynamics is complicated. We say a chaotic…
One or more small holes provide non-destructive windows to observe corresponding closed systems, for example by measuring long time escape rates of particles as a function of hole sizes and positions. To leading order the escape rate of…
We provide a brief survey of quantum statistical characterisations of order, disorder and coherence in systems of many degrees of freedom. Here, order and coherence are described in terms of symmetry breakdown, while disorder is described…
We introduce a novel approach for controlling fast chaos in time-delay dynamical systems and use it to control a chaotic photonic device with a characteristic time scale of ~12 ns. Our approach is a prescription for how to implement…
The sequences, given by a 7D map have been analysed by means of the methods, widely used to detect chaos in the real world in order to test their sensitivity to chaotic features of a non-linear system determined by comparatively high number…
Synchronization of chaos arises between coupled dynamical systems and is very well understood as a temporal phenomena which leads the coupled systems to converge or develop a dependence with time. In this work, we provide a complementary…
Many definitions of chaos have appeared in the last decades and with them the question if they are equivalent in some more specific spaces. Our focus will be distributional chaos, first defined in 1994 and later subdivided into three major…
Chaos is widely understood as being a consequence of sensitive dependence upon initial conditions. This is the result of an instability in phase space, which separates trajectories exponentially. Here, we demonstrate that this criterion…
The study of dynamics in general relativity has been hampered by a lack of coordinate independent measures of chaos. Here I review a variety of invariant measures for quantifying chaotic dynamics in relativity that exploit the coordinate…
Complexity is an interdisciplinary concept which, first of all, addresses the question of how order emerges out of randomness. For many reasons matrices provide a very practical and powerful tool in approaching and quantifying the related…
We show how a simple scheme of symbolic dynamics distinguishes a chaotic from a random time series and how it can be used to detect structural relationships in coupled dynamics. This is relevant for the question at which scale in complex…
We examine whether the chaotic behavior of classical systems with a limited number of degrees of freedom can produce quantum dephasing, against the conventional idea that dephasing takes place only in large systems with a huge number of…
We present an introduction to the study of chaos in discrete and continuous dynamical systems using the CAS Maxima. These notes are intended to cover the standard topics and techniques: discrete and continuous logistic equation to model…
Interrelations between dynamical and statistical laws in physics, on the one hand, and between the classical and quantum mechanics, on the other hand, are discussed with emphasis on the new phenomenon of dynamical chaos. The principal…
In experiments, the dynamical behavior of systems is reflected in time series. Due to the finiteness of the observational data set it is not possible to reconstruct the invariant measure up to arbitrary fine resolution and arbitrary high…
A simple method to perform chaos control without the need of complex numerical and analytical calculations is proposed. The method works for dynamical systems with bounded solutions and in the trivial case of constant Jacobians.
This contribution is relative to the opening lectures of the ISSAOS 2001 summer school and it has the aim to provide the reader with some concepts and techniques concerning chaotic dynamics and transport processes in fluids. Our intention…
The problem of characterizing complexity of quantum dynamics - in particular of locally interacting chains of quantum particles - will be reviewed and discussed from several different perspectives: (i) stability of motion against external…