| Title:
|
Bifurcations for Turing instability without SO(2) symmetry (English) |
| Author:
|
Ogawa, Toshiyuki |
| Author:
|
Okuda, Takashi |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
43 |
| Issue:
|
6 |
| Year:
|
2007 |
| Pages:
|
869-877 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, we consider the Swift–Hohenberg equation with perturbed boundary conditions. We do not a priori know the eigenfunctions for the linearized problem since the ${\rm SO(2)}$ symmetry of the problem is broken by perturbation. We show that how the neutral stability curves change and, as a result, how the bifurcation diagrams change by the perturbation of the boundary conditions. (English) |
| Keyword:
|
perturbed boundary conditions |
| Keyword:
|
imperfect pitchfork bifurcation |
| Keyword:
|
Turing instability |
| MSC:
|
35B32 |
| MSC:
|
35K20 |
| MSC:
|
35K55 |
| MSC:
|
37G40 |
| MSC:
|
37L10 |
| MSC:
|
37L20 |
| idZBL:
|
Zbl 1136.37042 |
| idMR:
|
MR2388400 |
| . |
| Date available:
|
2009-09-24T20:30:36Z |
| Last updated:
|
2013-09-21 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135822 |
| . |
| Reference:
|
[1] Carr J.: Applications of Center Manifold Theory.Springer–Verlag, Berlin 1981 MR 0635782 |
| Reference:
|
[2] Dillon R., Maini P. K., Othmer H. G.: Pattern formation in generalized Turing systems I.Steady-state patterns in systems with mixed boundary conditions. J. Math. Biol. 32 (1994), 345–393 Zbl 0829.92001, MR 1279745 |
| Reference:
|
[3] Kabeya Y., Morishita, H., Ninomiya H.: Imperfect bifurcations arising from elliptic boundary value problems.Nonlinear Anal. 48 (2002), 663–684 Zbl 1017.34041, MR 1868109, 10.1016/S0362-546X(00)00205-4 |
| Reference:
|
[4] Kato Y., Fujimura K.: Folded solution branches in Rayleigh–Bénard convection in the presence of avoided crossings of neutral stability curves.J. Phys. Soc. Japan 75 (2006), 3, 034401–034405 10.1143/JPSJ.75.034401 |
| Reference:
|
[5] Mizushima J., Nakamura T.: Repulsion of eigenvalues in the Rayleigh–Bénard problem.J. Phys. Soc. Japan 71 (2002), 3, 677–680 Zbl 1161.76483, 10.1143/JPSJ.71.677 |
| Reference:
|
[6] Nishiura Y.: Far-from-Equilibrium Dynamics, Translations of Mathematical Monographs 209, Americal Mathematical Society, Rhode Island 200. MR 1903642 |
| Reference:
|
[7] Ogawa T., Okuda T.: Bifurcation analysis to Swift–Hohenberg equation with perturbed boundary conditions.In preparation Zbl 1221.37157 |
| Reference:
|
[8] Tuckerman L., Barkley D.: Bifurcation analysis of the Eckhaus instability.Phys. D 46 (1990), 57–86 Zbl 0721.35008, MR 1078607, 10.1016/0167-2789(90)90113-4 |
| . |
