Avoiding Dynamical Degradation in Computer Simulation of Chaotic Systems Using Semi-Explicit Integration: Rössler Oscillator Case
Dynamical degradation is a known problem in the computer simulation of chaotic systems. Data type limitations, sampling, and rounding errors give rise to the periodic behavior. In applications of chaotic systems in secure communication and cryptography systems, such effects can reduce data storage s...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-11-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/5/4/214 |
| _version_ | 1827672340190724096 |
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| author | Aleksandra Tutueva Denis Butusov |
| author_facet | Aleksandra Tutueva Denis Butusov |
| author_sort | Aleksandra Tutueva |
| collection | DOAJ |
| description | Dynamical degradation is a known problem in the computer simulation of chaotic systems. Data type limitations, sampling, and rounding errors give rise to the periodic behavior. In applications of chaotic systems in secure communication and cryptography systems, such effects can reduce data storage security and operation. In this study, we considered a possible solution to this problem by using semi-explicit integration. The key idea is to perturb the chaotic trajectory by switching between two integrators, which possess close but still different numerical solutions. Compared with the traditional approach based on the perturbation of the bifurcation parameter, this technique does not significantly change the nonlinear properties of the system. We verify the efficiency of the proposed perturbation method through several numerical experiments using the well-known Rössler oscillator. |
| first_indexed | 2024-03-10T04:05:09Z |
| format | Article |
| id | doaj.art-35c2ef9e4a244418ad2032f1f61245b3 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-10T04:05:09Z |
| publishDate | 2021-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-35c2ef9e4a244418ad2032f1f61245b32023-11-23T08:23:51ZengMDPI AGFractal and Fractional2504-31102021-11-015421410.3390/fractalfract5040214Avoiding Dynamical Degradation in Computer Simulation of Chaotic Systems Using Semi-Explicit Integration: Rössler Oscillator CaseAleksandra Tutueva0Denis Butusov1Department of Computer-Aided Design, Saint Petersburg Electrotechnical University “LETI”, 197376 Saint Petersburg, RussiaYouth Research Institute, Saint Petersburg Electrotechnical University “LETI”, 197376 Saint Petersburg, RussiaDynamical degradation is a known problem in the computer simulation of chaotic systems. Data type limitations, sampling, and rounding errors give rise to the periodic behavior. In applications of chaotic systems in secure communication and cryptography systems, such effects can reduce data storage security and operation. In this study, we considered a possible solution to this problem by using semi-explicit integration. The key idea is to perturb the chaotic trajectory by switching between two integrators, which possess close but still different numerical solutions. Compared with the traditional approach based on the perturbation of the bifurcation parameter, this technique does not significantly change the nonlinear properties of the system. We verify the efficiency of the proposed perturbation method through several numerical experiments using the well-known Rössler oscillator.https://www.mdpi.com/2504-3110/5/4/214dynamic degradationsemi-explicit integrationfinite precision arithmeticlinear feedback shift registerchaotic systemRössler attractor |
| spellingShingle | Aleksandra Tutueva Denis Butusov Avoiding Dynamical Degradation in Computer Simulation of Chaotic Systems Using Semi-Explicit Integration: Rössler Oscillator Case Fractal and Fractional dynamic degradation semi-explicit integration finite precision arithmetic linear feedback shift register chaotic system Rössler attractor |
| title | Avoiding Dynamical Degradation in Computer Simulation of Chaotic Systems Using Semi-Explicit Integration: Rössler Oscillator Case |
| title_full | Avoiding Dynamical Degradation in Computer Simulation of Chaotic Systems Using Semi-Explicit Integration: Rössler Oscillator Case |
| title_fullStr | Avoiding Dynamical Degradation in Computer Simulation of Chaotic Systems Using Semi-Explicit Integration: Rössler Oscillator Case |
| title_full_unstemmed | Avoiding Dynamical Degradation in Computer Simulation of Chaotic Systems Using Semi-Explicit Integration: Rössler Oscillator Case |
| title_short | Avoiding Dynamical Degradation in Computer Simulation of Chaotic Systems Using Semi-Explicit Integration: Rössler Oscillator Case |
| title_sort | avoiding dynamical degradation in computer simulation of chaotic systems using semi explicit integration rossler oscillator case |
| topic | dynamic degradation semi-explicit integration finite precision arithmetic linear feedback shift register chaotic system Rössler attractor |
| url | https://www.mdpi.com/2504-3110/5/4/214 |
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