Dynamics of two interfaces in a hybrid system with jump-type heterogeneity

Kei Nishi, Yasumasa Nishiura, Takashi Teramoto

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)

Abstract

We consider the dynamics of two interfaces that interact through a continuous medium with spatial heterogeneity. The dynamics of interface positions is governed by ordinary differential equations (ODEs), whereas that of the continuous field by a partial differential equation. The resulting mixed ODE-PDE system, which we call a hybrid system (HS), is derived as a singular limit of a certain bistable reaction-diffusion system (PDE), describing the dynamics of traveling pulses of front-back type. First, the traveling pulse dynamics in the heterogeneous medium is numerically studied both for the bistable reaction-diffusion system and for the hybrid system. Then, the hybrid system is analyzed to clarify the underlying mechanisms for the pulse behavior observed. In particular, we carry out a center manifold reduction for the hybrid system, which reveals not only the supercriticality of Hopf bifurcations but also the mechanism for sliding motion of an oscillating pulse observed in the heterogeneous medium.

Original languageEnglish
Pages (from-to)351-395
Number of pages45
JournalJapan Journal of Industrial and Applied Mathematics
Volume30
Issue number2
DOIs
Publication statusPublished - 2013 Jun

Keywords

  • Center manifold reduction
  • Heterogeneous media
  • Interface dynamics
  • Reaction-diffusion system

ASJC Scopus subject areas

  • Engineering(all)
  • Applied Mathematics

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