The analysis of observed chaotic data in physical systems

HDI Abarbanel, R Brown, JJ Sidorowich… - Reviews of modern …, 1993 - APS
Chaotic time series data are observed routinely in experiments on physical systems and in
observations in the field. The authors review developments in the extraction of information of …

Delayed feedback control of chaos

K Pyragas - … Transactions of the Royal Society A …, 2006 - royalsocietypublishing.org
Time-delayed feedback control is well known as a practical method for stabilizing unstable
periodic orbits embedded in chaotic attractors. The method is based on applying feedback …

A practical method for calculating largest Lyapunov exponents from small data sets

MT Rosenstein, JJ Collins, CJ De Luca - Physica D: Nonlinear Phenomena, 1993 - Elsevier
Detecting the presence of chaos in a dynamical system is an important problem that is
solved by measuring the largest Lyapunov exponent. Lyapunov exponents quantify the …

Lyapunov characteristic exponents for smooth dynamical systems and for Hamiltonian systems; a method for computing all of them. Part 1: Theory

G Benettin, L Galgani, A Giorgilli, JM Strelcyn - Meccanica, 1980 - Springer
Summary Since several years Lyapunov Characteristic Exponents are of interest in the study
of dynamical systems in order to characterize quantitatively their stochasticity properties …

The Lyapunov characteristic exponents and their computation

C Skokos - Dynamics of Small Solar System Bodies and …, 2009 - Springer
We present a survey of the theory of the Lyapunov Characteristic Exponents (LCEs) for
dynamical systems, as well as of the numerical techniques developed for the computation of …

[КНИГА][B] Foundations of synergetics I: Distributed active systems

AS Mikhailov - 2012 - books.google.com
This book gives an introduction to the mathematical theory of cooperative behavior in active
systems of various origins, both natural and artificial. It is based on a lecture course in …

Control of chaos via extended delay feedback

K Pyragas - Physics letters A, 1995 - Elsevier
We present a linear analysis for a recently proposed modification of the delay feedback
control technique that allows one to stabilize unstable periodic orbits of a strange attractor …

Prediction in chaotic nonlinear systems: Methods for time series with broadband Fourier spectra

HDI Abarbanel, R Brown, JB Kadtke - Physical Review A, 1990 - APS
We consider the problem of prediction and system identification for time series having
broadband power spectra that arise from the intrinsic nonlinear dynamics of the system. We …

[КНИГА][B] Computational methods in bifurcation theory and dissipative structures

M Kubicek, M Marek - 2012 - books.google.com
" Dissipative structures" is a concept which has recently been used in physics to discuss the
formation of structures organized in space and/or time at the expense of the energy flowing …

[КНИГА][B] Nonlinear dynamics and quantum chaos

S Wimberger - 2014 - Springer
Sandro Wimberger An Introduction Second Edition Page 1 Nonlinear Dynamics and
Quantum Chaos Sandro Wimberger An Introduction Second Edition Graduate Texts in …