Bifurcation analysis of a diffusion-ODE model with Turing instability and hysteresis
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 spatiall...
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
7 July 2017
|
| In: |
Hiroshima mathematical journal
Year: 2017, Jahrgang: 47, Heft: 2, Pages: 217-247 |
| ISSN: | 2758-9641 |
| Online-Zugang: | Verlag, kostenfrei, Volltext: http://projecteuclid.org/euclid.hmj/1499392826 Verlag, kostenfrei, Volltext: http://projecteuclid.org/download/pdf_1/euclid.hmj/1499392826 
|
| Verfasserangaben: | Ying Li, Anna Marciniak-Czochra, Izumi Takagi, Boying Wu |
| Zusammenfassung: | 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. |
|---|---|
| Beschreibung: | Gesehen am 26.07.2017 |
| Beschreibung: | Online Resource |
| ISSN: | 2758-9641 |