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Keywords:
perturbed boundary conditions; imperfect pitchfork bifurcation; Turing instability
perturbed boundary conditions; imperfect pitchfork bifurcation; Turing instability
Summary:
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.
References:
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