Quantifying Chaos by Various Computational Methods. Part 1: Simple Systems; Entropy; Vol. 20
| Parent link: | Entropy Vol. 20.— 2018.— [175, 28 p.] |
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| Awdur Corfforaethol: | |
| Awduron Eraill: | , , , , , |
| Crynodeb: | 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. |
| Iaith: | Saesneg |
| Cyhoeddwyd: |
2018
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| Pynciau: | |
| Mynediad Ar-lein: | https://doi.org/10.3390/e20030175 |
| Fformat: | Electronig Pennod Llyfr |
| KOHA link: | https://koha.lib.tpu.ru/cgi-bin/koha/opac-detail.pl?biblionumber=666983 |
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| 200 | 1 | |a Quantifying Chaos by Various Computational Methods. Part 1: Simple Systems |f J. Awrejcewicz, A. V. Krysko, N. P. Erofeev [et al.] | |
| 203 | |a Text |c electronic | ||
| 300 | |a Title screen | ||
| 320 | |a [References: 35 tit.] | ||
| 330 | |a 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. | ||
| 461 | |t Entropy | ||
| 463 | |t Vol. 20 |v [175, 28 p.] |d 2018 | ||
| 610 | 1 | |a электронный ресурс | |
| 610 | 1 | |a труды учёных ТПУ | |
| 610 | 1 | |a Lyapunov exponents | |
| 610 | 1 | |a Wolf method | |
| 610 | 1 | |a Rosenstein method | |
| 610 | 1 | |a Kantz method | |
| 610 | 1 | |a neural network method | |
| 610 | 1 | |a method of synchronization | |
| 610 | 1 | |a Benettin method | |
| 610 | 1 | |a Fourier spectrum | |
| 610 | 1 | |a Gauss wavelets | |
| 701 | 1 | |a Awrejcewicz |b J. |g Jan | |
| 701 | 1 | |a Krysko |b A. V. |c specialist in the field of Informatics and computer engineering |c programmer Tomsk Polytechnic University, Professor, doctor of physico-mathematical Sciences |f 1967- |g Anton Vadimovich |3 (RuTPU)RU\TPU\pers\36883 | |
| 701 | 1 | |a Erofeev |b N. P. |g Nikolay Pavlovich | |
| 701 | 1 | |a Dobriyan |b V. V. |g Vitaly Vyacheslavovich | |
| 701 | 1 | |a Barulina |b M. A. |g Marina Aleksandrovna | |
| 701 | 1 | |a Krysko |b V. A. |g Vadim | |
| 712 | 0 | 2 | |a Национальный исследовательский Томский политехнический университет |b Институт кибернетики |b Кафедра инженерной графики и промышленного дизайна |b Научно-учебная лаборатория 3D моделирования |3 (RuTPU)RU\TPU\col\20373 |
| 801 | 2 | |a RU |b 63413507 |c 20220210 |g RCR | |
| 856 | 4 | |u https://doi.org/10.3390/e20030175 | |
| 942 | |c CF | ||