Bifurcations for Turing instability without SO(2) symmetry
Toshiyuki Ogawa; Takashi Okuda
Kybernetika (2007)
- Volume: 43, Issue: 6, page 869-877
- ISSN: 0023-5954
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topOgawa, Toshiyuki, and Okuda, Takashi. "Bifurcations for Turing instability without SO(2) symmetry." Kybernetika 43.6 (2007): 869-877. <http://eudml.org/doc/33903>.
@article{Ogawa2007,
abstract = {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.},
author = {Ogawa, Toshiyuki, Okuda, Takashi},
journal = {Kybernetika},
keywords = {perturbed boundary conditions; imperfect pitchfork bifurcation; Turing instability; Swift-Hohenberg equation with perturbed boundary conditions; neutral stability curves; bifurcation diagrams; imperfect pitchfork bifurcation; linearized eigenvalue problem},
language = {eng},
number = {6},
pages = {869-877},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Bifurcations for Turing instability without SO(2) symmetry},
url = {http://eudml.org/doc/33903},
volume = {43},
year = {2007},
}
TY - JOUR
AU - Ogawa, Toshiyuki
AU - Okuda, Takashi
TI - Bifurcations for Turing instability without SO(2) symmetry
JO - Kybernetika
PY - 2007
PB - Institute of Information Theory and Automation AS CR
VL - 43
IS - 6
SP - 869
EP - 877
AB - 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.
LA - eng
KW - perturbed boundary conditions; imperfect pitchfork bifurcation; Turing instability; Swift-Hohenberg equation with perturbed boundary conditions; neutral stability curves; bifurcation diagrams; imperfect pitchfork bifurcation; linearized eigenvalue problem
UR - http://eudml.org/doc/33903
ER -
References
top- Carr J., Applications of Center Manifold Theory, Springer–Verlag, Berlin 1981 MR0635782
- 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 (1994) Zbl0829.92001MR1279745
- Kabeya Y., Morishita, H., Ninomiya H., 10.1016/S0362-546X(00)00205-4, Nonlinear Anal. 48 (2002), 663–684 Zbl1017.34041MR1868109DOI10.1016/S0362-546X(00)00205-4
- Kato Y., Fujimura K., 10.1143/JPSJ.75.034401, J. Phys. Soc. Japan 75 (2006), 3, 034401–034405 DOI10.1143/JPSJ.75.034401
- Mizushima J., Nakamura T., 10.1143/JPSJ.71.677, J. Phys. Soc. Japan 71 (2002), 3, 677–680 Zbl1161.76483DOI10.1143/JPSJ.71.677
- Nishiura Y., Far-from-Equilibrium Dynamics, Translations of Mathematical Monographs 209, Americal Mathematical Society, Rhode Island 200 MR1903642
- Ogawa T., Okuda T., Bifurcation analysis to Swift–Hohenberg equation with perturbed boundary conditions, In preparation Zbl1221.37157
- Tuckerman L., Barkley D., 10.1016/0167-2789(90)90113-4, Phys. D 46 (1990), 57–86 (1990) Zbl0721.35008MR1078607DOI10.1016/0167-2789(90)90113-4
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