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...
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| Main Authors: | , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
7 July 2017
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| In: |
Hiroshima mathematical journal
Year: 2017, Volume: 47, Issue: 2, Pages: 217-247 |
| ISSN: | 2758-9641 |
| Online Access: | Verlag, kostenfrei, Volltext: http://projecteuclid.org/euclid.hmj/1499392826 Verlag, kostenfrei, Volltext: http://projecteuclid.org/download/pdf_1/euclid.hmj/1499392826 
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| Author Notes: | Ying Li, Anna Marciniak-Czochra, Izumi Takagi, Boying Wu |
| Summary: | 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. |
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| Item Description: | Gesehen am 26.07.2017 |
| Physical Description: | Online Resource |
| ISSN: | 2758-9641 |