具有Michaelis-Menten饱和函数的趋化模型的Turing分岔分析
Turing Bifurcation Analysis of Chemotaxis Model with Michaelis-Menten Saturation Function
摘要: 本文研究了一类具有Michaelis-Menten饱和函数的趋化模型，以趋化性系数为参数，分析了系统在齐次Neumann边界条件下的Turing分岔行为。首先通过对系统在正平衡点处的特征方程进行讨论，得到了正平衡点的稳定性和Turing分岔的存在性。其次利用中心流形和正则形式理论，得到了Turing分岔的稳定性和分岔方向。最后，通过数值模拟验证了理论分析结果。
Abstract: In this paper, we investigate a chemotaxis models with Michaelis-Menten saturation functions subject to the homogeneous Neumann boundary condition. And discussed the Turing bifurcation by choosing the chemotaxis coefficient as the bifurcation parameter. The stability of the positive equilibrium and the existence of Turing bifurcation are obtained by the analysis of the corresponding characteristic equation. Moreover, we derive the stability and direction of the Turing bifurcation by using center manifold and normal form theory. Some numerical simulations are also carried out to illustrate the theoretical results.
文章引用：任倍佳, 邱焕焕. 具有Michaelis-Menten饱和函数的趋化模型的Turing分岔分析[J]. 应用数学进展, 2024, 13(12): 5136-5146. https://doi.org/10.12677/aam.2024.1312496

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