Geodesic
Bifurcations for Turing instability without SO(2) symmetry
Kybernetika, Tome 43 (2007) no. 6, pp. 869-877.

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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 ${\rm SO(2)}$ 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.
Classification : 35B32, 35K20, 35K55, 37G40, 37L10, 37L20
Keywords: perturbed boundary conditions; imperfect pitchfork bifurcation; Turing instability 
@article{KYB_2007__43_6_a10,
     author = {Ogawa, Toshiyuki and Okuda, Takashi},
     title = {Bifurcations for {Turing} instability without {SO(2)} symmetry},
     journal = {Kybernetika},
     pages = {869--877},
     publisher = {mathdoc},
     volume = {43},
     number = {6},
     year = {2007},
     mrnumber = {2388400},
     zbl = {1136.37042},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2007__43_6_a10/}
}
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Ogawa, Toshiyuki; Okuda, Takashi. Bifurcations for Turing instability without SO(2) symmetry. Kybernetika, Tome 43 (2007) no. 6, pp. 869-877. http://geodesic.mathdoc.fr/item/KYB_2007__43_6_a10/