Bifurcation analysis of a diffusion-ODE model with turing instability and hysteresis

Ying Li, Anna Marciniak-Czochra, Izumi Takagi, Boying Wu

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)

Abstract

This paper is devoted to the existence and (in)stability of nonconstant steady-states in a system of a semilinear parabolic equation coupled to an ODE, which is a simplified version of a receptor-ligand model of pattern formation. In the neighborhood of a constant steady-state, we construct spatially heterogeneous steady-states by applying the bifurcation theory. We also study the structure of the spectrum of the linearized operator and show that bifurcating steady-states are unstable against high wave number disturbances. In addition, we consider the global behavior of the bifurcating branches of nonconstant steady-states. These are quite different from classical reaction-diffusion systems where all species diffuse.

Original languageEnglish
Pages (from-to)217-247
Number of pages31
JournalHiroshima Mathematical Journal
Volume47
Issue number2
DOIs
Publication statusPublished - 2017 Jul

Keywords

  • Bifurcation analysis
  • Global behavior of solution branches
  • Instability
  • Pattern formation
  • Reaction-diffusion-ODE system
  • Steady-states

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

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