Dynamic bifurcation of the n-dimensional complex Swift-Hohenberg equation

doi:10.1007/s10483-010-1308-6

Applied Mathematics and Mechanics (English Edition) ›› 2010, Vol. 31 ›› Issue (6): 739-750.doi: https://doi.org/10.1007/s10483-010-1308-6

Dynamic bifurcation of the n-dimensional complex Swift-Hohenberg equation

肖庆坤高洪俊

Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210046, P. R. China

收稿日期:2009-11-18 修回日期:2010-05-08 出版日期:2010-06-01 发布日期:2010-06-01

Dynamic bifurcation of the n-dimensional complex Swift-Hohenberg equation

XIAO Qing-Kun, GAO Hong-Jun

Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210046, P. R. China

Received:2009-11-18 Revised:2010-05-08 Online:2010-06-01 Published:2010-06-01

摘要/Abstract

摘要： This paper is concerned with the bifurcation of a complex Swift-Hohenberg equation. The attractor bifurcation of the complex Swift-Hohenberg equation on a onedimensional domain (0, L) is investigated. It is shown that the n-dimensional complex Swift-Hohenberg equation bifurcates from the trivial solution to an attractor under the Dirichlet boundary condition on a general domain and under a periodic boundary condition when the bifurcation parameter crosses some critical values. The stability property of the bifurcation attractor is analyzed.

关键词: Swift-Hohenberg equation, bifurcation, stability, center manifold

Abstract: This paper is concerned with the bifurcation of a complex Swift-Hohenberg equation. The attractor bifurcation of the complex Swift-Hohenberg equation on a onedimensional domain (0, L) is investigated. It is shown that the n-dimensional complex Swift-Hohenberg equation bifurcates from the trivial solution to an attractor under the Dirichlet boundary condition on a general domain and under a periodic boundary condition when the bifurcation parameter crosses some critical values. The stability property of the bifurcation attractor is analyzed.

Key words: Swift-Hohenberg equation, bifurcation, stability, center manifold

中图分类号:

肖庆坤高洪俊. Dynamic bifurcation of the n-dimensional complex Swift-Hohenberg equation[J]. Applied Mathematics and Mechanics (English Edition), 2010, 31(6): 739-750.

XIAO Qing-Kun;GAO Hong-Jun. Dynamic bifurcation of the n-dimensional complex Swift-Hohenberg equation[J]. Applied Mathematics and Mechanics (English Edition), 2010, 31(6): 739-750.

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Dynamic bifurcation of the n-dimensional complex Swift-Hohenberg equation

Dynamic bifurcation of the n-dimensional complex Swift-Hohenberg equation

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