| SPATIO-TEMPORAL CHAOTIC SYNCHRONIZATION FOR MODES COUPLED TWO GINZBURG-LANDAU EQUATIONS |
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| 引用本文： | 胡满峰,徐振源. SPATIO-TEMPORAL CHAOTIC SYNCHRONIZATION FOR MODES COUPLED TWO GINZBURG-LANDAU EQUATIONS[J]. 应用数学和力学(英文版), 2006, 27(8): 1149-1156. DOI: 10.1007/s 10483-006-0816-y |
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| 作者姓名： | 胡满峰 徐振源 |
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| 作者单位： | School of Science Southern Yangtze University Wuxi 214122 Jiangsu Province P. R. China，School of Science，Southern Yangtze University Wuxi 214122 Jiangsu Province P. R. China |
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| 摘 要： | On the basis of numerical computation, the conditions of the modes coupling are proposed, and the high-frequency modes are coupled, but the low frequency modes are uncoupled. It is proved that there exist an absorbing set and a global finite dimensional attractor which is compact and connected in the function space for the high-frequency modes coupled two Ginzburg-Landau equations(MGLE). The trajectory of driver equation may be spatio-temporal chaotic. One associates with MGLE, a truncated form of the equations. The prepared equations persist in long time dynamical behavior of MGLE. MGLE possess the squeezing properties under some conditions. It is proved that the complete spatio-temporal chaotic synchronization for MGLE can occur. Synchronization phenomenon of infinite dimensional dynamical system (IFDDS) is illustrated on the mathematical theory qualitatively. The method is different from Liapunov function methods and approximate linear methods.
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| 关 键 词： | 完整同步化 Ginzberg-Landau方程 吸引子 时空混沌 |
| 文章编号： | 10.0007/s10483-006-0816-y |
| 收稿时间： | 2004-08-17 |
| 修稿时间： | 2006-02-24 |
Spatio-temporal chaotic synchronization for modes coupled two Ginzburg-Landau equations |
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| Man-feng Hu,Zhen-yuan Xu. Spatio-temporal chaotic synchronization for modes coupled two Ginzburg-Landau equations[J]. Applied Mathematics and Mechanics(English Edition), 2006, 27(8): 1149-1156. DOI: 10.1007/s 10483-006-0816-y |
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| Authors: | Man-feng Hu Zhen-yuan Xu |
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| Affiliation: | School of Science,Southern Yangtze University,Wuxi 214122,Jiangsu Province,P.R.China |
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| Abstract: | On the basis of numerical computation, the conditions of the modes coupling are proposed, and the high-frequency modes are coupled, but the low frequency modes are uncoupled. It is proved that there exist an absorbing set and a global finite dimensional attractor which is compact and connected in the function space for the high-frequency modes coupled two Ginzburg-Landau equations(MGLE). The trajectory of driver equation may be spatio-temporal chaotic. One associates with MGLE, a truncated form of the equations. The prepared equations persist in long time dynamical behavior of MGLE. MGLE possess the squeezing properties under some conditions. It is proved that the complete spatio-temporal chaotic synchronization for MGLE can occur. Synchronization phenomenon of infinite dimensional dynamical system (IFDDS) is illustrated on the mathematical theory qualitatively. The method is different from Liapunov function methods and approximate linear methods. |
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| Keywords: | complete synchronization Ginzberg-Landau equations attractor spatio-temporal chaos |
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