| n维复Swift-Hohenberg方程的动态分叉 |
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| 引用本文： | 肖庆坤,高洪俊.n维复Swift-Hohenberg方程的动态分叉[J].应用数学和力学,2010,31(6):710-721. |
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| 作者姓名： | 肖庆坤 高洪俊 |
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| 作者单位： | 南京师范大学 数学科学学院 数学研究所,南京 210046 |
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| 基金项目： | 国家自然科学基金，江苏省研究生培养创新工程2009年度资助项目 |
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| 摘 要： | 考虑复Swift-Hohenberg方程的分叉问题．首先对复Swift-Hohenberg方程在一维区域(0,L)上的吸引子分叉进行了考虑．而后给出了n维复Swift-Hohenberg方程,在一般区域上Dirichlet边界条件下和周期边界条件下,当参数λ穿过某些分叉点时从平凡解处分叉出吸引子,并对吸引子分叉的稳定性进行了分析．
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| 关 键 词： | Swift-Hohenberg方程 分叉 稳定性 中心流形 |
| 收稿时间： | 1900-01-01 |
Dynamic Bifurcation of the n-Dimensional Complex Swift-Hohenberg Equation |
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| XIAO Qing-kun,GAO Hong-jun.Dynamic Bifurcation of the n-Dimensional Complex Swift-Hohenberg Equation[J].Applied Mathematics and Mechanics,2010,31(6):710-721. |
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| Authors: | XIAO Qing-kun GAO Hong-jun |
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| Institution: | Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210046, P. R. China |
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| Abstract: | The bifurcation of the complex Swif-tHohenberg equation was considered. A ttractor bifurcation of the complex S wift-Hohenberg equation on a one-dmiensional domain (0, L) was investigated. It's also shown that then-dmiens ionalcomplex Swift-Hohenberg equation bifurcates from the trivial solution to an attractor under the Dirichlet boundary condition on a general doma in and under the periodic boundary condition when the bifurcation parameter Kcrosses some critical value. The stability property of the bifurcation attractor is also analyzed. |
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