Journal ArticleDOI
Lyapunov Characteristic Exponents for smooth dynamical systems and for hamiltonian systems; A method for computing all of them. Part 2: Numerical application
TLDR
In this article, the authors give an explicit method for computing all Lyapunov Characteristic Exponents of a dynamical system, together with some numerical examples for mappings on manifolds and for Hamiltonian systems.Abstract:
The present paper, together with the previous one (Part 1: Theory, published in this journal) is intended to give an explicit method for computing all Lyapunov Characteristic Exponents of a dynamical system. After the general theory on such exponents developed in the first part, in the present paper the computational method is described (Chapter A) and some numerical examples for mappings on manifolds and for Hamiltonian systems are given (Chapter B).read more
Citations
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Heterogeneous beliefs and routes to chaos in a simple asset pricing model
William A. Brock,Cars Hommes +1 more
TL;DR: In this paper, the authors investigate the dynamics in a simple present discounted value asset pricing model with heterogeneous beliefs, where agents choose from a finite set of predictors of future prices of a risky asset and revise their "beliefs" in each period in a boundedly rational way, according to a fitness measure such as past realized profits.
Journal ArticleDOI
The analysis of observed chaotic data in physical systems
TL;DR: Chaotic time series data are observed routinely in experiments on physical systems and in observations in the field as mentioned in this paper, and many tools have been developed for the analysis of such data.
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.
Journal ArticleDOI
Anomalous scaling laws in multifractal objects
TL;DR: In this paper, the authors describe anomalous scaling in terms of multifractal objects, defined by a measure whose scaling properties are characterized by a family of singularities, which are identified by a scaling exponent.
Journal ArticleDOI
Recurrent neural networks employing Lyapunov exponents for EEG signals classification
TL;DR: The obtained results demonstrated that the proposed RNNs employing the Lyapunov exponents can be useful in analyzing long-term EEG signals for early detection of the electroencephalographic changes.
References
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Journal ArticleDOI
Deterministic nonperiodic flow
TL;DR: In this paper, it was shown that nonperiodic solutions are ordinarily unstable with respect to small modifications, so that slightly differing initial states can evolve into considerably different states, and systems with bounded solutions are shown to possess bounded numerical solutions.
Journal ArticleDOI
A Two-dimensional Mapping with a Strange Attractor
TL;DR: In this article, the same properties can be observed in a simple mapping of the plane defined by: \({x i + 1}} = {y_i} + 1 - ax_i^2,{y i+ 1} = b{x_i}\).
Journal ArticleDOI
The applicability of the third integral of motion: Some numerical experiments
Michel Henon,Carl Heiles +1 more
TL;DR: In this paper, the existence of a third isolating integral of motion in an axisymmetric potential was investigated by numerical experiments and it was found that the third integral exists for only a limited rage of initial conditions.
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.
Journal ArticleDOI
Kolmogorov entropy and numerical experiments
TL;DR: In this paper, a numerical study of the Kolmogorov entropy for the H\'enon-Heiles model is presented, based on mathematical results of Oseledec and Piesin.