Bifurcation analysis of a diffusion-ODE model with Turing instability and hysteresis
Bifurcation analysis of a diffusion-ODE model with Turing instability and hysteresis
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DOI：
10.32917/hmj/1499392826
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发表时间：
2017-07
影响因子：
0.2
通讯作者：
Yingguo Li;A. Marciniak-Czochra;I. Takagi;Boying Wu
中科院分区：
文献类型：
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作者：
Yingguo Li;A. Marciniak-Czochra;I. Takagi;Boying Wu
摘要。本文研究了半线性抛物方程耦合到ODE系统的非常稳态的存在性和稳定性，该系统是图案形成的受体-配体模型的简化版本。在常稳态的邻域中，应用分岔理论构造空间非均质稳态。我们还研究了线性化算子的谱结构，并证明了分岔稳态在高波数扰动下是不稳定的。此外，我们还考虑了非常稳态分岔分支的全局行为。这与所有物种都使用的经典反应-扩散系统有很大的不同。
A bstract . 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 di¤erent from classical reaction-di¤usion systems where all species di¤use.