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

• Verfasst von: Li, Ying [VerfasserIn]
• Verfasst von: Marciniak-Czochra, Anna [VerfasserIn]
• Verfasst von: Takagi, Izumi [VerfasserIn]
• Titel: Bifurcation analysis of a diffusion-ODE model with Turing instability and hysteresis
• Verf.angabe: Ying Li, Anna Marciniak-Czochra, Izumi Takagi, Boying Wu
• Umfang: 31 S.
• Fussnoten: Gesehen am 26.07.2017
• Titel Quelle: Enthalten in: Hiroshima mathematical journal
• Jahr Quelle: 2017
• Band/Heft Quelle: 47(2017), 2, S. 217-247
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1561205540

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.