Dynamic Bifurcation of the n-Dimensional Complex Swift-Hohenberg Equation
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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
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.-
Key words:
- Swift-Hohen berg equation /
- bifurcation /
- stability /
- center manifold
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