Hyperchaos in a Conservative System with Nonhyperbolic Fixed Points
Chaotic dynamics exists in many natural systems, such as weather and climate, and there are many applications in different disciplines. However, there are few research results about chaotic conservative systems especially the smooth hyperchaotic conservative system in both theory and application. Th...
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2018-01-01
|
| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2018/9430637 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832563672245862400 |
|---|---|
| author | Aiguo Wu Shijian Cang Ruiye Zhang Zenghui Wang Zengqiang Chen |
| author_facet | Aiguo Wu Shijian Cang Ruiye Zhang Zenghui Wang Zengqiang Chen |
| author_sort | Aiguo Wu |
| collection | DOAJ |
| description | Chaotic dynamics exists in many natural systems, such as weather and climate, and there are many applications in different disciplines. However, there are few research results about chaotic conservative systems especially the smooth hyperchaotic conservative system in both theory and application. This paper proposes a five-dimensional (5D) smooth autonomous hyperchaotic system with nonhyperbolic fixed points. Although the proposed system includes four linear terms and four quadratic terms, the new system shows complicated dynamics which has been proven by the theoretical analysis. Several notable properties related to conservative systems and the existence of perpetual points are investigated for the proposed system. Moreover, its conservative hyperchaotic behavior is illustrated by numerical techniques including phase portraits and Lyapunov exponents. |
| format | Article |
| id | doaj-art-f11a84c224824e2d879b7bdb86d4e4bf |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-f11a84c224824e2d879b7bdb86d4e4bf2025-02-03T01:13:03ZengWileyComplexity1076-27871099-05262018-01-01201810.1155/2018/94306379430637Hyperchaos in a Conservative System with Nonhyperbolic Fixed PointsAiguo Wu0Shijian Cang1Ruiye Zhang2Zenghui Wang3Zengqiang Chen4School of Electrical Engineering and Automation, Tianjin University, Tianjin 300072, ChinaSchool of Electrical Engineering and Automation, Tianjin University, Tianjin 300072, ChinaSchool of Electrical Engineering and Automation, Tianjin University, Tianjin 300072, ChinaDepartment of Electrical and Mining Engineering, University of South Africa, Florida 1710, South AfricaCollege of Computer and Control Engineering, Nankai University, Tianjin 300071, ChinaChaotic dynamics exists in many natural systems, such as weather and climate, and there are many applications in different disciplines. However, there are few research results about chaotic conservative systems especially the smooth hyperchaotic conservative system in both theory and application. This paper proposes a five-dimensional (5D) smooth autonomous hyperchaotic system with nonhyperbolic fixed points. Although the proposed system includes four linear terms and four quadratic terms, the new system shows complicated dynamics which has been proven by the theoretical analysis. Several notable properties related to conservative systems and the existence of perpetual points are investigated for the proposed system. Moreover, its conservative hyperchaotic behavior is illustrated by numerical techniques including phase portraits and Lyapunov exponents.http://dx.doi.org/10.1155/2018/9430637 |
| spellingShingle | Aiguo Wu Shijian Cang Ruiye Zhang Zenghui Wang Zengqiang Chen Hyperchaos in a Conservative System with Nonhyperbolic Fixed Points Complexity |
| title | Hyperchaos in a Conservative System with Nonhyperbolic Fixed Points |
| title_full | Hyperchaos in a Conservative System with Nonhyperbolic Fixed Points |
| title_fullStr | Hyperchaos in a Conservative System with Nonhyperbolic Fixed Points |
| title_full_unstemmed | Hyperchaos in a Conservative System with Nonhyperbolic Fixed Points |
| title_short | Hyperchaos in a Conservative System with Nonhyperbolic Fixed Points |
| title_sort | hyperchaos in a conservative system with nonhyperbolic fixed points |
| url | http://dx.doi.org/10.1155/2018/9430637 |
| work_keys_str_mv | AT aiguowu hyperchaosinaconservativesystemwithnonhyperbolicfixedpoints AT shijiancang hyperchaosinaconservativesystemwithnonhyperbolicfixedpoints AT ruiyezhang hyperchaosinaconservativesystemwithnonhyperbolicfixedpoints AT zenghuiwang hyperchaosinaconservativesystemwithnonhyperbolicfixedpoints AT zengqiangchen hyperchaosinaconservativesystemwithnonhyperbolicfixedpoints |