[논문]Bifurcation Analysis and Pattern Selection of Solutions for the Modified Swift-Hohenberg Equation

Choi, Yuncherl; Ha, Taeyoung; Han, Jongmin

doi:10.1142/s0218127420300311

[해외논문] Bifurcation Analysis and Pattern Selection of Solutions for the Modified Swift-Hohenberg Equation

International journal of bifurcation and chaos in applied sciences and engineering, v.30 no.11, 2020년, pp.2030031 -

Choi, Yuncherl (Ingenium College of Liberal Arts, Kwangwoon University, Seoul 01891, Korea) , Ha, Taeyoung (Division of Medical Mathematics, National Institute for Mathematical Sciences, Daejeon 34047, Korea) , Han, Jongmin (Department of Mathematics, Kyung Hee University, Seoul 02447, Korea)

Abstract ▼ AI-Helper

In this paper, motivated by [Peletier & Rottschäfer, 2004; Peletier & Williams, 2007], we study the dynamical bifurcation of the modified Swift-Hohenberg equation endowed with an evenly periodic condition on the interval $ [-\lambda ,\lambda ]$. As $ \lambda $ crosses over the critical points, the trivial solution bifurcates to an attractor and some new patterns of solutions emerge. We provide detailed descriptions of all possible final patterns of solutions on the overlapped intervals of $ \lambda $, which emerge after a gap collapses to a point. We also compute all critical values of $ \lambda $, $ N$ and $ \mu $ precisely, which are responsible for bifurcation and pattern formations. We finally provide numerical results that explain the main theorems.

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