June  2009, 11(4): 875-891. doi: 10.3934/dcdsb.2009.11.875

Dynamic bifurcation of the complex Swift-Hohenberg equation

1. 

Department of Mathematics, Hankuk University of Foreign Studies, Yongin, Kyounggi-do, 449-791, South Korea

2. 

Department of Mathematics, Indiana University, Rawles Hall, Bloomington IN 47405

Received  June 2008 Revised  February 2009 Published  April 2009

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.
Citation: Jongmin Han, Masoud Yari. Dynamic bifurcation of the complex Swift-Hohenberg equation. Discrete & Continuous Dynamical Systems - B, 2009, 11 (4) : 875-891. doi: 10.3934/dcdsb.2009.11.875
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