Dynamic bifurcation of the complex Swift-Hohenberg equation

Jongmin Han; Masoud Yari

doi:10.3934/dcdsb.2009.11.875

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2009, Volume 11, Issue 4: 875-891. Doi: 10.3934/dcdsb.2009.11.875

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Dynamic bifurcation of the complex Swift-Hohenberg equation

Jongmin Han^1, and
Masoud Yari^2,

1.
Department of Mathematics, Hankuk University of Foreign Studies, Yongin, Kyounggi-do, 449-791
2.
Department of Mathematics, Indiana University, Rawles Hall, Bloomington IN 47405

Received: May 31, 2008

Revised: January 31, 2009

Published: October 2009

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Abstract

In this paper we are concerned with the dynamic bifurcation of the complex Swift-Hohenberg equation on a closed interval in $\mathbb R$. We consider the equations under the Dirichlet and the periodic boundary conditions. It is shown that the equation bifurcates from the trivial solution to an attractor when the control parameter crosses the critical value.

Keywords:

complex Swift-Hohenberg equation,
attractor bifurcation.

Mathematics Subject Classification: Primary: 37G35; Secondary: 35G25.

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