Global bifurcation structure on a shadow system with a source term-representation of all solutions

Hideaki Takaichi, Izumi Takagi, Shoji Yotsutani

Research output: Contribution to journalArticlepeer-review

Abstract

As the first step to understand the Gierer-Meinhardt system with source term, it is important to know the global bifurcation diagram of a shadow system. For the case without source term, it is well-understood. However, for the case with source term, the shadow system has a nonlocal term. Thus standard methods do not work, and there are a few partial results even for one-dimensional case. We give explicit representations of all solutions in terms of elliptic functions. They play crucial roles to clarify the global bifurcation diagram.

Original languageEnglish
Pages (from-to)1344-1350
Number of pages7
JournalDiscrete and Continuous Dynamical Systems- Series A
Issue numberSUPPL.
Publication statusPublished - 2011 Sep 1

Keywords

  • Parameter representation
  • Reaction diffusion
  • Stationary

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics
  • Analysis

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