Bifurcations for Turing instability without SO(2) symmetry

Toshiyuki Ogawa; Takashi Okuda

Kybernetika (2007)

  • Volume: 43, Issue: 6, page 869-877
  • ISSN: 0023-5954

Abstract

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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 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.

How to cite

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Ogawa, 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

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  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 (1994) Zbl0829.92001MR1279745
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  6. Nishiura Y., Far-from-Equilibrium Dynamics, Translations of Mathematical Monographs 209, Americal Mathematical Society, Rhode Island 200 MR1903642
  7. Ogawa T., Okuda T., Bifurcation analysis to Swift–Hohenberg equation with perturbed boundary conditions, In preparation Zbl1221.37157
  8. 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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