n维复Swift-Hohenberg方程的动态分叉

肖庆坤; 高洪俊

doi:10.3879/j.issn.1000-0887.2010.06.008

n维复Swift-Hohenberg方程的动态分叉

doi: 10.3879/j.issn.1000-0887.2010.06.008

南京师范大学数学科学学院数学研究所,南京 210046

基金项目: 国家自然科学基金资助项目(10871097);江苏省研究生培养创新工程2009年度资助项目(CX09B-296Z)

详细信息

作者简介:
肖庆坤(1983- ),男,山东人,博士生(E-mail:xiaoqingkun@hotmail.com);高洪俊(联系人.Te:l+86-25-85898771;E-mail:gaohj@njnu.edu.cn).

中图分类号: O175
计量
- 文章访问数: 1571
- HTML全文浏览量: 148
- PDF下载量: 768
- 被引次数: 0
出版历程
- 收稿日期: 1900-01-01
- 修回日期: 2010-05-10
- 刊出日期: 2010-06-15

Dynamic Bifurcation of the n-Dimensional Complex Swift-Hohenberg Equation

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

摘要

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．
- 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.
- Swift-Hohen berg equation /
- bifurcation /
- stability /
- center manifold

HTML全文

参考文献(17)

[1]	Swift J B, Hohenberg P C. Hydrodynamic fluctuations at the convective instability [J]. Phys Rev A, 1977, 15(1): 319-328. doi: 10.1103/PhysRevA.15.319
[2]	Peletier L A, Williams J F. Some canonical bifurcations in the Swift-Hohenberg equation [J].SIAM J Appl Dyn Syst, 2007, 6(1): 208-235. doi: 10.1137/050647232
[3]	Peletier L A, Rottschfer V. Pattern selection of solutions of the Swift-Hohenberg equation [J].Phys D, 2004,194(1/2): 95-126. doi: 10.1016/j.physd.2004.01.043
[4]	Peletier L A, Rottschfer V. Large time behaviour of solutions of the Swift-Hohenberg equation [J].C R Math Acad Sci Paris, 2003, 336(3): 225-230. doi: 10.1016/S1631-073X(03)00021-9
[5]	Collet P, Eckmann J P. Instabilities and Fronts in Extended Systems[M].Princeton Series in Physics. New Jersey:Princeton University Press, 1990.
[6]	Budd C J, Kuske R. Localized periodic patterns for the non-symmetric generalized Swift-Hohenberg equation [J].Phys D, 2005, 208(1/2): 73-95. doi: 10.1016/j.physd.2005.06.009
[7]	Cross M C, Hohenberg P C. Pattern formation outside of equilibrium [J].Rev Mod Phys, 1993,65(3): 851-1112. doi: 10.1103/RevModPhys.65.851
[8]	Buceta J, Lindenberg K, Parrondo J M R. Stationary and oscillatory spatial patterns induced by global periodic switching[J].Phys Rev Lett,2001, 88(2): 024103. doi: 10.1103/PhysRevLett.88.024103
[9]	Tribelskii M I. Short wavelength instability and transition to chaos in distributed systems with additional symmetry [J]. Phys Uspekhi, 1997, 40(2): 159-180. doi: 10.1070/PU1997v040n02ABEH000193
[10]	Hohenberg P C, Swift J B. Effects of additive noise at the onset of Rayleigh-Bénard convection [J].Phys Rev A, 1992, 46(8): 4773-4785. doi: 10.1103/PhysRevA.46.4773
[11]	Staliunas K, Sanchez-Morcillo V J. Dynamics of phase domains in the Swift-Hohenberg equation [J].Phys Lett A, 1998, 241(1): 28-34. doi: 10.1016/S0375-9601(98)00084-X
[12]	Aranson I, Assenheimer M, Steinberg V. Large-scale flow and spiral core instability in Rayleigh-Bénard convection [J].Phys Rev E,1997, 55(5): R4877-R4880.
[13]	Yari M. Attractor bifurcation and final patterns of the n-dimensional and generalized Swift-Hohenberg equations [J]. Discr Contin Dyn Syst, Ser B,2007, 7(2): 441-456.
[14]	Han J, Yari M. Dynamic bifurcation of the complex Swift-Hohenberg equation [J].Discr Contin Dyn Syst , Ser B,2009, 11(4): 875-891. doi: 10.3934/dcdsb.2009.11.875
[15]	Ma T, Wang S. Bifurcation Theory and Applications[M]. Nonlinear Science Ser A. Vol 53.New Jersey: World Scientific, 2005.
[16]	Ma T, Wang S. Dynamic bifurcation of nonlinear evolution equations [J]. Chin Ann Math B,2005, 26(2): 185-206. doi: 10.1142/S0252959905000166
[17]	Chen Y J, Gao H J, Zhu Y P. Exponential attractors for the complex Swift-Hohenberg equation in some Banach spaces [J].Acta Math Appl Sinica, 2007, 30(4): 699-706.