| 000 | 03225nlm1a2200481 4500 | ||
|---|---|---|---|
| 001 | 666983 | ||
| 005 | 20231030042055.0 | ||
| 035 | _a(RuTPU)RU\TPU\network\38187 | ||
| 090 | _a666983 | ||
| 100 | _a20220210a2018 k y0engy50 ba | ||
| 101 | 0 | _aeng | |
| 102 | _aCH | ||
| 135 | _adrcn ---uucaa | ||
| 181 | 0 | _ai | |
| 182 | 0 | _ab | |
| 200 | 1 |
_aQuantifying Chaos by Various Computational Methods. Part 1: Simple Systems _fJ. Awrejcewicz, A. V. Krysko, N. P. Erofeev [et al.] |
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| 203 |
_aText _celectronic |
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| 300 | _aTitle screen | ||
| 320 | _a[References: 35 tit.] | ||
| 330 | _aThe 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 | _tEntropy | ||
| 463 |
_tVol. 20 _v[175, 28 p.] _d2018 |
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| 610 | 1 | _aэлектронный ресурс | |
| 610 | 1 | _aтруды учёных ТПУ | |
| 610 | 1 | _aLyapunov exponents | |
| 610 | 1 | _aWolf method | |
| 610 | 1 | _aRosenstein method | |
| 610 | 1 | _aKantz method | |
| 610 | 1 | _aneural network method | |
| 610 | 1 | _amethod of synchronization | |
| 610 | 1 | _aBenettin method | |
| 610 | 1 | _aFourier spectrum | |
| 610 | 1 | _aGauss wavelets | |
| 701 | 1 |
_aAwrejcewicz _bJ. _gJan |
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| 701 | 1 |
_aKrysko _bA. V. _cspecialist in the field of Informatics and computer engineering _cprogrammer Tomsk Polytechnic University, Professor, doctor of physico-mathematical Sciences _f1967- _gAnton Vadimovich _2stltpush _3(RuTPU)RU\TPU\pers\36883 |
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| 701 | 1 |
_aErofeev _bN. P. _gNikolay Pavlovich |
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| 701 | 1 |
_aDobriyan _bV. V. _gVitaly Vyacheslavovich |
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| 701 | 1 |
_aBarulina _bM. A. _gMarina Aleksandrovna |
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| 701 | 1 |
_aKrysko _bV. A. _gVadim |
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| 712 | 0 | 2 |
_aНациональный исследовательский Томский политехнический университет _bИнститут кибернетики _bКафедра инженерной графики и промышленного дизайна _bНаучно-учебная лаборатория 3D моделирования _h6704 _2stltpush _3(RuTPU)RU\TPU\col\20373 |
| 801 | 2 |
_aRU _b63413507 _c20220210 _gRCR |
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| 856 | 4 | _uhttps://doi.org/10.3390/e20030175 | |
| 942 | _cCF | ||