DYNAMIC BIFURCATION OF THE PERIODIC SWIFT-HOHENBERG EQUATION

Jongmin Han; Masoud Yari

doi:10.4134/BKMS.2012.49.5.923

DYNAMIC BIFURCATION OF THE PERIODIC SWIFT-HOHENBERG EQUATION

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Abstract

In this paper we study the dynamic bifurcation of the Swift-Hohenberg equation on a periodic cell Ω = [−L, L]. It is shown that the equations bifurcates from the trivial solution to an attractor A_λ when the control parameter λ crosses the critical value. In the odd periodic case, A_λ is homeomorphic to S¹ and consists of eight singular points and their connecting orbits. In the periodic case, A_λ is homeomorphic to S¹, and contains a torus and two circles which consist of singular points.

Original language	English
Pages (from-to)	923-937
Number of pages	15
Journal	Bulletin of the Korean Mathematical Society
Volume	49
Issue number	5
DOIs	https://doi.org/10.4134/BKMS.2012.49.5.923
Publication status	Published - Mar 2024

Bibliographical note

Publisher Copyright:
© 2012 The Korean Mathematical Society.

Keywords

attractor bifurcation
Swift-Hohenberg equation

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10.4134/BKMS.2012.49.5.923

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title = "DYNAMIC BIFURCATION OF THE PERIODIC SWIFT-HOHENBERG EQUATION",

abstract = "In this paper we study the dynamic bifurcation of the Swift-Hohenberg equation on a periodic cell Ω = [−L, L]. It is shown that the equations bifurcates from the trivial solution to an attractor Aλ when the control parameter λ crosses the critical value. In the odd periodic case, Aλ is homeomorphic to S1 and consists of eight singular points and their connecting orbits. In the periodic case, Aλ is homeomorphic to S1, and contains a torus and two circles which consist of singular points.",

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author = "Jongmin Han and Masoud Yari",

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AU - Yari, Masoud

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N2 - In this paper we study the dynamic bifurcation of the Swift-Hohenberg equation on a periodic cell Ω = [−L, L]. It is shown that the equations bifurcates from the trivial solution to an attractor Aλ when the control parameter λ crosses the critical value. In the odd periodic case, Aλ is homeomorphic to S1 and consists of eight singular points and their connecting orbits. In the periodic case, Aλ is homeomorphic to S1, and contains a torus and two circles which consist of singular points.

AB - In this paper we study the dynamic bifurcation of the Swift-Hohenberg equation on a periodic cell Ω = [−L, L]. It is shown that the equations bifurcates from the trivial solution to an attractor Aλ when the control parameter λ crosses the critical value. In the odd periodic case, Aλ is homeomorphic to S1 and consists of eight singular points and their connecting orbits. In the periodic case, Aλ is homeomorphic to S1, and contains a torus and two circles which consist of singular points.

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JF - Bulletin of the Korean Mathematical Society

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ER -

DYNAMIC BIFURCATION OF THE PERIODIC SWIFT-HOHENBERG EQUATION

Abstract

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Keywords

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