Related papers: How Can We Observe and Describe Chaos?
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…
We present some new results which relate information to chaotic dynamics. In our approach the quantity of information is measured by the Algorithmic Information Content (Kolmogorov complexity) or by a sort of computable version of it…
Modern software-based services are implemented as distributed systems with complex behavior and failure modes. Many large tech organizations are using experimentation to verify the reliability of such systems. We use the term "Chaos…
We explore the concept of scaling invariance in a type of dynamical systems that undergo a transition from order (regularity) to disorder (chaos). The systems are described by a two-dimensional, nonlinear mapping that preserves the area in…
Non-deterministic chaos is a form of low-dimensional dynamics which is characterized by the existence of a countable set of {\em sensitive decision points} (SDP's). Away from these points, the dynamics is well-behaved. Near these points,…
This paper summarises a numerical investigation of how the usual manifestations of chaos and regularity for flows in time-independent Hamiltonians can be alterred by a systematic time-dependence of the form arising naturally in an expanding…
In order to analyze the effect of chaos or order on the rate of decoherence in a subsystem we aim to distinguish effects of the two types of dynamics from those depending on the choice of the wave packet. To isolate the former we introduce…
The complexity and the chaos degree can be used to examine the chaotic aspects of not only several nonlinear classical and quantum physical physics but also life sciences. We will construct a model describing the function of brain in the…
The problem of separation of an observed sum of chaotic signals into the individual components in the presence of noise on the path to the observer is considered. A noise threshold is found above which high-quality separation is impossible.…
Scientists often think of the world (or some part of it) as a dynamical system, a stochastic process, or a generalization of such a system. Prominent examples of systems are (i) the system of planets orbiting the sun or any other classical…
Chaos as typical property of non-linear systems has revealed its crucial role in various problems of astrophysics and cosmology. The problems discussed at these lectures include planetary dynamics, galactic dynamics, reconstruction of the…
Observability can determine which recorded variables of a given system are optimal for discriminating its different states. Quantifying observability requires knowledge of the equations governing the dynamics. These equations are often…
Signatures of chaos can be understood by studying quantum systems whose classical counterpart is chaotic. However, the concepts of integrability, non-integrability and chaos extend to systems without a classical analogue. Here, we first…
Systems that exhibit complex behaviours are often found in a particular dynamical condition, poised between order and disorder. This observation is at the core of the so-called criticality hypothesis, which states that systems in a…
We discuss how to characterize the behavior of a chaotic dynamical system depending on a parameter that varies periodically in time. In particular, we study the predictability time, the correlations and the mean responses, by defining a…
We investigate the connections between microscopic chaos, defined on a dynamical level and arising from collisions between molecules, and diffusion, characterized by a mean square displacement proportional to the time. We use a number of…
We here describe the possibility of a synthetic description of the onset of Chaos in many degrees of freedom dynamical systems within the framework of the geometric description of dynamics. We show how this approach to instability helps to…
The Mackey--Glass equation, which was proposed to illustrate nonlinear phenomena in physiological control systems, is a classical example of a simple looking time delay system with very complicated behavior. Here we use a novel approach for…
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.…
This paper aims to cast some new light on controlling chaos using the OGY- and the Zero-Spectral-Radius methods. In deriving those methods we use a generalized procedure differing from the usual ones. This procedure allows us to…