Journal ArticleDOI
A comparative study of computation of Lyapunov spectra with different algorithms
K. Ramasubramanian,M. S. Sriram +1 more
TLDR
The standard method seems to be the most efficient followed by the new method and the differential version of the standard method (in that order), as far as the CPU time for the computation of the Lyapunov spectra is concerned.About:
This article is published in Physica D: Nonlinear Phenomena.The article was published on 2000-05-01. It has received 196 citations till now. The article focuses on the topics: Lyapunov exponent & Lyapunov function.read more
Citations
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Book
Regular and Chaotic Dynamics
TL;DR: In this article, a self consistent treatment of the subject at the graduate level and as a reference for scientists already working in the field is presented. But the focus is on the mechanics for generating chaotic motion, methods of calculating the transitions from regular to chaotic motion and the dynamical and statistical properties of the dynamics when it is chaotic.
Journal ArticleDOI
A novel chaos-based image encryption using DNA sequence operation and Secure Hash Algorithm SHA-2
TL;DR: The theoretical analysis and experimental results show that the algorithm improves the encoding efficiency, enhances the security of the ciphertext and has a large key space and a high key sensitivity, and it is able to resist against the statistical and exhaustive attacks.
Journal ArticleDOI
Synchronization of the fractional order hyperchaos Lorenz systems with activation feedback control
Xingyuan Wang,Jun-Mei Song +1 more
TL;DR: In this article, the synchronization conditions of fractional order chaotic systems with activation feedback method were analyzed and the synchronization of commensurate order hyperchaotic Lorenz system of the base order 0.98 was implemented based on this method.
Book ChapterDOI
The Lyapunov Characteristic Exponents and Their Computation
TL;DR: A survey of the theory of the Lyapunov Characteristic Exponents (LCEs) for dynamical systems, as well as numerical techniques developed for the computation of the maximal, of few and of all of them, can be found in this article.
Book ChapterDOI
The Lyapunov Characteristic Exponents and their computation
TL;DR: 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 the maximal, of few and of all of them, is presented.
References
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Journal ArticleDOI
Determining Lyapunov exponents from a time series
TL;DR: In this article, the authors present the first algorithms that allow the estimation of non-negative Lyapunov exponents from an experimental time series, which provide a qualitative and quantitative characterization of dynamical behavior.
Book
Chaos in classical and quantum mechanics
TL;DR: In this article, the three-body problem: Moon-Earth-Sun, Three Methods of Section, Periodic Orbits, and Surface of Solution is considered, as well as the Diamagnetic Kepler Problem.
Journal ArticleDOI
Construction of higher order symplectic integrators
TL;DR: For Hamiltonian systems of the form H = T(p)+V(q) a method was shown to construct explicit and time reversible symplectic integrators of higher order as discussed by the authors.
Journal ArticleDOI
Lyapunov Characteristic Exponents for smooth dynamical systems and for hamiltonian systems; a method for computing all of them. Part 1: Theory
TL;DR: In this paper, a method for computing all of the Lyapunov characteristic exponents of order greater than one is presented, which is related to the increase of volumes of a dynamical system.