Dynamics of a New Hyperchaotic System with Only One Equilibrium Point
A new 4D hyperchaotic system is constructed based on the Lorenz system. The compound structure and forming mechanism of the new hyperchaotic attractor are studied via a controlled system with constant controllers. Furthermore, it is found that the Hopf bifurcation occurs in this hyperchaotic system...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/935384 |
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| _version_ | 1832556966595002368 |
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| author | Xiang Li Ranchao Wu |
| author_facet | Xiang Li Ranchao Wu |
| author_sort | Xiang Li |
| collection | DOAJ |
| description | A new 4D hyperchaotic system is constructed based on the Lorenz system. The compound structure and forming mechanism of the new hyperchaotic attractor are studied via a controlled system with constant controllers. Furthermore, it is found that the Hopf bifurcation occurs in this
hyperchaotic system when the bifurcation parameter exceeds a critical value. The direction of the Hopf bifurcation as well as the stability of bifurcating periodic solutions is presented in detail by virtue of the normal form theory. Numerical simulations are given to illustrate and verify the results. |
| format | Article |
| id | doaj-art-96033ba4688641a58aa535db22000e5c |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-96033ba4688641a58aa535db22000e5c2025-02-03T05:43:59ZengWileyJournal of Mathematics2314-46292314-47852013-01-01201310.1155/2013/935384935384Dynamics of a New Hyperchaotic System with Only One Equilibrium PointXiang Li0Ranchao Wu1School of Mathematics, Anhui University, Hefei 230039, ChinaSchool of Mathematics, Anhui University, Hefei 230039, ChinaA new 4D hyperchaotic system is constructed based on the Lorenz system. The compound structure and forming mechanism of the new hyperchaotic attractor are studied via a controlled system with constant controllers. Furthermore, it is found that the Hopf bifurcation occurs in this hyperchaotic system when the bifurcation parameter exceeds a critical value. The direction of the Hopf bifurcation as well as the stability of bifurcating periodic solutions is presented in detail by virtue of the normal form theory. Numerical simulations are given to illustrate and verify the results.http://dx.doi.org/10.1155/2013/935384 |
| spellingShingle | Xiang Li Ranchao Wu Dynamics of a New Hyperchaotic System with Only One Equilibrium Point Journal of Mathematics |
| title | Dynamics of a New Hyperchaotic System with Only One Equilibrium Point |
| title_full | Dynamics of a New Hyperchaotic System with Only One Equilibrium Point |
| title_fullStr | Dynamics of a New Hyperchaotic System with Only One Equilibrium Point |
| title_full_unstemmed | Dynamics of a New Hyperchaotic System with Only One Equilibrium Point |
| title_short | Dynamics of a New Hyperchaotic System with Only One Equilibrium Point |
| title_sort | dynamics of a new hyperchaotic system with only one equilibrium point |
| url | http://dx.doi.org/10.1155/2013/935384 |
| work_keys_str_mv | AT xiangli dynamicsofanewhyperchaoticsystemwithonlyoneequilibriumpoint AT ranchaowu dynamicsofanewhyperchaoticsystemwithonlyoneequilibriumpoint |