Quantifying Chaos by Various Computational Methods. Part 1: Simple Systems

Quantifying Chaos by Various Computational Methods. Part 1: Simple Systems

Bibliografische gegevens
Parent link:Entropy
Vol. 20.— 2018.— [175, 28 p.]
Coauteur: Национальный исследовательский Томский политехнический университет Институт кибернетики Кафедра инженерной графики и промышленного дизайна Научно-учебная лаборатория 3D моделирования
Andere auteurs: Awrejcewicz J. Jan, Krysko A. V. Anton Vadimovich, Erofeev N. P. Nikolay Pavlovich, Dobriyan V. V. Vitaly Vyacheslavovich, Barulina M. A. Marina Aleksandrovna, Krysko V. A. Vadim
Samenvatting:Title screen
The aim of the paper was to analyze the given nonlinear problem by different methods of computation of the Lyapunov exponents (Wolf method, Rosenstein method, Kantz method, the method based on the modification of a neural network, and the synchronization method) for the classical problems governed by difference and differential equations (Hйnon map, hyperchaotic Hйnon map, logistic map, Rцssler attractor, Lorenz attractor) and with the use of both Fourier spectra and Gauss wavelets. It has been shown that a modification of the neural network method makes it possible to compute a spectrum of Lyapunov exponents, and then to detect a transition of the system regular dynamics into chaos, hyperchaos, and others. The aim of the comparison was to evaluate the considered algorithms, study their convergence, and also identify the most suitable algorithms for specific system types and objectives. Moreover, an algorithm of calculation of the spectrum of Lyapunov exponents based on a trained neural network has been proposed. It has been proven that the developed method yields good results for different types of systems and does not require a priori knowledge of the system equations.
Taal:Engels
Gepubliceerd in: 2018
Onderwerpen:
электронный ресурс
труды учёных ТПУ
Lyapunov exponents
Wolf method
Rosenstein method
Kantz method
neural network method
method of synchronization
Benettin method
Fourier spectrum
Gauss wavelets
Online toegang:https://doi.org/10.3390/e20030175
Formaat: Elektronisch Hoofdstuk
KOHA link:https://koha.lib.tpu.ru/cgi-bin/koha/opac-detail.pl?biblionumber=666983

Gelijkaardige items

Gelijkaardige items