DYNAMIC BIFURCATION OF THE PERIODIC SWIFT-HOHENBERG EQUATION

Title & Authors
DYNAMIC BIFURCATION OF THE PERIODIC SWIFT-HOHENBERG EQUATION
Han, Jong-Min; Yari, Masoud;

Abstract
In this paper we study the dynamic bifurcation of the Swift-Hohenberg equation on a periodic cell $\small{{\Omega}=[-L,L]}$. It is shown that the equations bifurcates from the trivial solution to an attractor $\small{\mathcal{A}_{\lambda}}$ when th control parameter $\small{{\lambda}}$ crosses the critical value. In the odd periodic case $\small{\mathcal{A}_{\lambda}}$ is homeomorphic to $\small{S^1}$ and consists of eight singular points and thei connecting orbits. In the periodic case, $\small{\mathcal{A}_{\lambda}}$ is homeomorphic to $\small{S^1}$, an contains a torus and two circles which consist of singular points.
Keywords
Swift-Hohenberg equation;attractor bifurcation;
Language
English
Cited by
1.
DYNAMICAL BIFURCATION OF THE ONE-DIMENSIONAL CONVECTIVE CAHN-HILLIARD EQUATION,;

Korean Journal of Mathematics, 2014. vol.22. 4, pp.621-632
2.
DYNAMICAL BIFURCATION OF THE ONE DIMENSIONAL MODIFIED SWIFT-HOHENBERG EQUATION,;

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DYNAMICAL BIFURCATION OF THE ONE DIMENSIONAL MODIFIED SWIFT-HOHENBERG EQUATION, Bulletin of the Korean Mathematical Society, 2015, 52, 4, 1241
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DYNAMICAL BIFURCATION OF THE ONE-DIMENSIONAL CONVECTIVE CAHN-HILLIARD EQUATION, Korean Journal of Mathematics, 2014, 22, 4, 621
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Dynamical Bifurcation of the Generalized Swift–Hohenberg Equation, International Journal of Bifurcation and Chaos, 2015, 25, 08, 1550095
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