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Bifurcations for Turing instability without SO(2) symmetry

Toshiyuki Ogawa, Takashi Okuda (2007)

Kybernetika

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.

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