Bulletin of the Korean Mathematical Society (대한수학회보)

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DYNAMIC BIFURCATION OF THE PERIODIC SWIFT-HOHENBERG EQUATION

  • Han, Jong-Min (Department of Mathematics Kyung Hee University) ;
  • Yari, Masoud (School of Mathematics Institute for Research in Fundamental Sciences (IPM))
  • Received : 2011.05.03
  • Published : 2012.09.30
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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 th 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 thei connecting orbits. In the periodic case, $\mathcal{A}_{\lambda}$ is homeomorphic to $S^1$, an contains a torus and two circles which consist of singular points.

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Acknowledgement

Supported by : Korea Research Foundation

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