Dynamical Bifurcation of the Generalized Swift-Hohenberg Equation

Yuncherl Choi; Jongmin Han; Jungho Park

doi:10.1142/S0218127415500959

Dynamical Bifurcation of the Generalized Swift-Hohenberg Equation

Yuncherl Choi
, Jongmin Han
, Jungho Park

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

5 Citations (Scopus)

Abstract

In this paper, we prove that the generalized Swift-Hohenberg equation bifurcates from the trivial states to an attractor as the control parameter α passes through critical points. The bifurcation is divided into two groups according to the dimension of the center manifolds. We show that the bifurcated attractor is homeomorphic to S¹ or S³ and it contains invariant circles of static solutions. We provide a criterion on the quadratic instability parameter μ which determines the bifurcation to be supercritical or subcritical.

Original language	English
Article number	1550095
Journal	International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume	25
Issue number	8
DOIs	https://doi.org/10.1142/S0218127415500959
Publication status	Published - 5 Jul 2015

Bibliographical note

Publisher Copyright:
© 2015 World Scientific Publishing Company.

Keywords

Generalized Swift-Hohenberg equation
dynamic bifurcation
second approximation formula

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10.1142/S0218127415500959

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abstract = "In this paper, we prove that the generalized Swift-Hohenberg equation bifurcates from the trivial states to an attractor as the control parameter α passes through critical points. The bifurcation is divided into two groups according to the dimension of the center manifolds. We show that the bifurcated attractor is homeomorphic to S1 or S3 and it contains invariant circles of static solutions. We provide a criterion on the quadratic instability parameter μ which determines the bifurcation to be supercritical or subcritical.",

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AU - Han, Jongmin

AU - Park, Jungho

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N2 - In this paper, we prove that the generalized Swift-Hohenberg equation bifurcates from the trivial states to an attractor as the control parameter α passes through critical points. The bifurcation is divided into two groups according to the dimension of the center manifolds. We show that the bifurcated attractor is homeomorphic to S1 or S3 and it contains invariant circles of static solutions. We provide a criterion on the quadratic instability parameter μ which determines the bifurcation to be supercritical or subcritical.

AB - In this paper, we prove that the generalized Swift-Hohenberg equation bifurcates from the trivial states to an attractor as the control parameter α passes through critical points. The bifurcation is divided into two groups according to the dimension of the center manifolds. We show that the bifurcated attractor is homeomorphic to S1 or S3 and it contains invariant circles of static solutions. We provide a criterion on the quadratic instability parameter μ which determines the bifurcation to be supercritical or subcritical.

KW - Generalized Swift-Hohenberg equation

KW - dynamic bifurcation

KW - second approximation formula

UR - https://www.scopus.com/pages/publications/84938105573

U2 - 10.1142/S0218127415500959

DO - 10.1142/S0218127415500959

M3 - Article

AN - SCOPUS:84938105573

SN - 0218-1274

VL - 25

JO - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

JF - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

IS - 8

M1 - 1550095

ER -

Dynamical Bifurcation of the Generalized Swift-Hohenberg Equation

Abstract

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Keywords

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