Reduction approach to the dynamics of interacting front solutions in a bistable reaction–diffusion system and its application to heterogeneous media

Kei Nishi, Yasumasa Nishiura, Takashi Teramoto

研究成果: Article査読

1 被引用数 (Scopus)

抄録

The dynamics of pulse solutions in a bistable reaction–diffusion system are studied analytically by reducing partial differential equations (PDEs) to finite-dimensional ordinary differential equations (ODEs). For the reduction, we apply the multiple-scales method to the mixed ODE–PDE system obtained by taking a singular limit of the PDEs. The reduced equations describe the interface motion of a pulse solution formed by two interacting front solutions. This motion is in qualitatively good agreement with that observed for the original PDE system. Furthermore, it is found that the reduction not only facilitates the analytical study of the pulse solution, especially the specification of the onset of local bifurcations, but also allows us to elucidate the global bifurcation structure behind the pulse behavior. As an application, the pulse dynamics in a heterogeneous bump-type medium are explored numerically and analytically. The reduced ODEs clarify the transition mechanisms between four pulse behaviors that occur at different parameter values.

本文言語English
ページ(範囲)183-207
ページ数25
ジャーナルPhysica D: Nonlinear Phenomena
398
DOI
出版ステータスPublished - 2019 11月

ASJC Scopus subject areas

  • 統計物理学および非線形物理学
  • 数理物理学
  • 凝縮系物理学
  • 応用数学

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