Chaotic Dynamics Analysis and FPGA Implementation Based on Gauss Legendre Integral
In this paper, we first design the corresponding integration algorithm and matlab program according to the Gauss–Legendre integration principle. Then, we select the Lorenz system, the Duffing system, the hidden attractor chaotic system and the Multi-wing hidden chaotic attractor system for chaotic d...
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| Format: | Article |
| Language: | English |
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MDPI AG
2025-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/13/2/201 |
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| author | Li Wen Li Cui Hairong Lin Fei Yu |
| author_facet | Li Wen Li Cui Hairong Lin Fei Yu |
| author_sort | Li Wen |
| collection | DOAJ |
| description | In this paper, we first design the corresponding integration algorithm and matlab program according to the Gauss–Legendre integration principle. Then, we select the Lorenz system, the Duffing system, the hidden attractor chaotic system and the Multi-wing hidden chaotic attractor system for chaotic dynamics analysis. We apply the Gauss–Legendre integral and the Runge–Kutta algorithm to the solution of dissipative chaotic systems for the first time and analyze and compare the differences between the two algorithms. Then, we propose for the first time a chaotic basin of the attraction estimation method based on the Gauss–Legendre integral and Lyapunov exponent and the decision criterion of this method. This method can better obtain the region of chaotic basin of attraction and can better distinguish the attractor and pseudo-attractor, which provides a new way for chaotic system analysis. Finally, we use FPGA technology to realize four corresponding chaotic systems based on the Gauss–Legendre integration algorithm. |
| format | Article |
| id | doaj-art-a3454bb9ccfc476c8ee55c705d925622 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-a3454bb9ccfc476c8ee55c705d9256222025-01-24T13:39:43ZengMDPI AGMathematics2227-73902025-01-0113220110.3390/math13020201Chaotic Dynamics Analysis and FPGA Implementation Based on Gauss Legendre IntegralLi Wen0Li Cui1Hairong Lin2Fei Yu3School of Information and Electrical Engineering, Hunan University of Science and Technology, Xiangtan 411201, ChinaSchool of Information and Electrical Engineering, Hunan University of Science and Technology, Xiangtan 411201, ChinaSchool of Electronic Information, Central South University, Changsha 410083, ChinaSchool of Computer and Communication Engineering, Changsha University of Science and Technology, Changsha 410114, ChinaIn this paper, we first design the corresponding integration algorithm and matlab program according to the Gauss–Legendre integration principle. Then, we select the Lorenz system, the Duffing system, the hidden attractor chaotic system and the Multi-wing hidden chaotic attractor system for chaotic dynamics analysis. We apply the Gauss–Legendre integral and the Runge–Kutta algorithm to the solution of dissipative chaotic systems for the first time and analyze and compare the differences between the two algorithms. Then, we propose for the first time a chaotic basin of the attraction estimation method based on the Gauss–Legendre integral and Lyapunov exponent and the decision criterion of this method. This method can better obtain the region of chaotic basin of attraction and can better distinguish the attractor and pseudo-attractor, which provides a new way for chaotic system analysis. Finally, we use FPGA technology to realize four corresponding chaotic systems based on the Gauss–Legendre integration algorithm.https://www.mdpi.com/2227-7390/13/2/201Gauss–Legendre integralbasin of attractionhidden attractor chaotic systemFPGA |
| spellingShingle | Li Wen Li Cui Hairong Lin Fei Yu Chaotic Dynamics Analysis and FPGA Implementation Based on Gauss Legendre Integral Mathematics Gauss–Legendre integral basin of attraction hidden attractor chaotic system FPGA |
| title | Chaotic Dynamics Analysis and FPGA Implementation Based on Gauss Legendre Integral |
| title_full | Chaotic Dynamics Analysis and FPGA Implementation Based on Gauss Legendre Integral |
| title_fullStr | Chaotic Dynamics Analysis and FPGA Implementation Based on Gauss Legendre Integral |
| title_full_unstemmed | Chaotic Dynamics Analysis and FPGA Implementation Based on Gauss Legendre Integral |
| title_short | Chaotic Dynamics Analysis and FPGA Implementation Based on Gauss Legendre Integral |
| title_sort | chaotic dynamics analysis and fpga implementation based on gauss legendre integral |
| topic | Gauss–Legendre integral basin of attraction hidden attractor chaotic system FPGA |
| url | https://www.mdpi.com/2227-7390/13/2/201 |
| work_keys_str_mv | AT liwen chaoticdynamicsanalysisandfpgaimplementationbasedongausslegendreintegral AT licui chaoticdynamicsanalysisandfpgaimplementationbasedongausslegendreintegral AT haironglin chaoticdynamicsanalysisandfpgaimplementationbasedongausslegendreintegral AT feiyu chaoticdynamicsanalysisandfpgaimplementationbasedongausslegendreintegral |