Dynamic bifurcation of the periodic Swift-Hohenberg equation
Bull. Korean Math. Soc. 2012 Vol. 49, No. 5, 923-937
https://doi.org/10.4134/BKMS.2012.49.5.923
Printed September 30, 2012
Jongmin Han and Masoud Yari
Kyung Hee University, Institute for Research in Fundamental Sciences (IPM)
Abstract : In this paper we study the dynamic bifurcation of the Swift-Hohenberg equation on a periodic cell $\Omega =[-L,L]$. It is shown that the equations bifurcates from the trivial solution to an attractor $\mathcal A_\lambda$ when the control parameter $\lambda$ crosses the critical value. In the odd periodic case, $\mathcal A_\lambda$ is homeomorphic to $S^1$ and consists of eight singular points and their connecting orbits. In the periodic case, $\mathcal A_\lambda$ is homeomorphic to $S^1$, and contains a torus and two circles which consist of singular points.
Keywords : Swift-Hohenberg equation, attractor bifurcation
MSC numbers : Primary 37G35, 35G25
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