KYBERNETIKA

Kybernetika 43(6):869-877, 2007.

Bifurcations for Turing Instability without So(2) Symmetry

Toshiyuki Ogawa and Takashi Okuda

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.

Keywords: perturbed boundary conditions; imperfect pitchfork bifurcation; Turing instability;

AMS: 37L10; 37L20; 35B32;