# Article

Full entry | PDF   (1.2 MB)
Keywords:
perturbed boundary conditions; imperfect pitchfork bifurcation; Turing instability
Summary:

References:
[1] Carr J.: Applications of Center Manifold Theory. Springer–Verlag, Berlin 1981 MR 0635782
[2] Dillon R., Maini P. K., Othmer H. G.: Pattern formation in generalized Turing systems I. Steady-state patterns in systems with mixed boundary conditions. J. Math. Biol. 32 (1994), 345–393 MR 1279745 | Zbl 0829.92001
[3] Kabeya Y., Morishita, H., Ninomiya H.: Imperfect bifurcations arising from elliptic boundary value problems. Nonlinear Anal. 48 (2002), 663–684 MR 1868109 | Zbl 1017.34041
[4] Kato Y., Fujimura K.: Folded solution branches in Rayleigh–Bénard convection in the presence of avoided crossings of neutral stability curves. J. Phys. Soc. Japan 75 (2006), 3, 034401–034405
[5] Mizushima J., Nakamura T.: Repulsion of eigenvalues in the Rayleigh–Bénard problem. J. Phys. Soc. Japan 71 (2002), 3, 677–680 Zbl 1161.76483
[6] Nishiura Y.: Far-from-Equilibrium Dynamics, Translations of Mathematical Monographs 209, Americal Mathematical Society, Rhode Island 200. MR 1903642
[7] Ogawa T., Okuda T.: Bifurcation analysis to Swift–Hohenberg equation with perturbed boundary conditions. In preparation Zbl 1221.37157
[8] Tuckerman L., Barkley D.: Bifurcation analysis of the Eckhaus instability. Phys. D 46 (1990), 57–86 MR 1078607 | Zbl 0721.35008

Partner of