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.
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 
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/
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     title = {Bifurcations for {Turing} instability without {SO(2)} symmetry},
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     pages = {869--877},
     year = {2007},
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     zbl = {1136.37042},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2007_43_6_a10/}
}
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