Bifurcation and final patterns of a modified swift-hohenberg equation

Yuncherl Choi; Taeyoung Ha; Jongmin Han; Doo Seok Lee

doi:10.3934/dcdsb.2017087

Bifurcation and final patterns of a modified swift-hohenberg equation

Yuncherl Choi, Taeyoung Ha, Jongmin Han, Doo Seok Lee

School of Undergraduate Studies

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

In this paper, we study the dynamical bifurcation and final patterns of a modified Swift-Hohenberg equation(MSHE). We prove that the MSHE bifurcates from the trivial solution to an S¹-attractor as the control parameter a passes through a critical number a. Using the center manifold analysis, we study the bifurcated attractor in detail by showing that it consists of finite number of singular points and their connecting orbits. We investigate the stability of those points. We also provide some numerical results supporting our analysis.

Original language	English
Pages (from-to)	2543-2567
Number of pages	25
Journal	Discrete and Continuous Dynamical Systems - Series B
Volume	22
Issue number	7
DOIs	https://doi.org/10.3934/dcdsb.2017087
State	Published - Sep 2017

Bibliographical note

Funding Information:
Y. Choi was supported by the Research Grant of Kwangwoon University in 2015. T. Ha was partially supported by the National Institute for Mathematical Sciences (NIMS) grant funded by the Korean government (No. A21300000). J. Han was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education, Science and Technology(2011-0008557).

Keywords

Center manifold
Dynamical bifurcation
Modified Swift-Hohenberg equation

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title = "Bifurcation and final patterns of a modified swift-hohenberg equation",

abstract = "In this paper, we study the dynamical bifurcation and final patterns of a modified Swift-Hohenberg equation(MSHE). We prove that the MSHE bifurcates from the trivial solution to an S1-attractor as the control parameter a passes through a critical number a. Using the center manifold analysis, we study the bifurcated attractor in detail by showing that it consists of finite number of singular points and their connecting orbits. We investigate the stability of those points. We also provide some numerical results supporting our analysis.",

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doi = "10.3934/dcdsb.2017087",

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AU - Han, Jongmin

AU - Lee, Doo Seok

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N2 - In this paper, we study the dynamical bifurcation and final patterns of a modified Swift-Hohenberg equation(MSHE). We prove that the MSHE bifurcates from the trivial solution to an S1-attractor as the control parameter a passes through a critical number a. Using the center manifold analysis, we study the bifurcated attractor in detail by showing that it consists of finite number of singular points and their connecting orbits. We investigate the stability of those points. We also provide some numerical results supporting our analysis.

AB - In this paper, we study the dynamical bifurcation and final patterns of a modified Swift-Hohenberg equation(MSHE). We prove that the MSHE bifurcates from the trivial solution to an S1-attractor as the control parameter a passes through a critical number a. Using the center manifold analysis, we study the bifurcated attractor in detail by showing that it consists of finite number of singular points and their connecting orbits. We investigate the stability of those points. We also provide some numerical results supporting our analysis.

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KW - Dynamical bifurcation

KW - Modified Swift-Hohenberg equation

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JO - Discrete and Continuous Dynamical Systems - Series B

JF - Discrete and Continuous Dynamical Systems - Series B

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ER -

Bifurcation and final patterns of a modified swift-hohenberg equation

Abstract

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Keywords

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