Chemotaxis-driven pattern formation for a reaction-diffusion-chemotaxis model with volume-filling effect
Chemotaxis-driven pattern formation for a reaction-diffusion-chemotaxis model with volume-filling effect
复制标题
具有体积填充效应的反应扩散趋化模型的趋化驱动模式形成
DOI：
10.1016/j.camwa.2016.06.039
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发表时间：
2016-09
影响因子：
2.9
通讯作者：
Han, Yazhou
中科院分区：
文献类型：
--
作者：
Ma, Manjun;Gao, Meiyan;Tong, Changqing;Han, Yazhou
In this paper we analytically and numerically investigate the emerging process of pattern formation for a reaction–diffusion–chemotaxis model with volume-filling effect. We first apply globally asymptotic stability analysis to show that the chemotactic flux is the key mechanism for pattern formation. Then, by weakly nonlinear analysis with multiple scales and the adjoint system theory, we derive the cubic and the quintic Stuart–Landau equations to describe the evolution of the amplitude of the most unstable mode, and thus the analytical approximate solutions of the patterns are obtained. Next, we present the selection law of principal wave mode of the emerging pattern by considering the competition of the growing modes, and for this we deduce the change rule of the most unstable mode and the coupled ordinary differential equations that indicates the significant nonlinear interaction of two competing modes. Finally, in the subcritical case we clarify that there exists the phenomenon of hysteresis, which implies the existence of large amplitude pattern for the bifurcation parameter values smaller than the first bifurcation point. Therefore, we answer the open problems proposed in the known references and improve some of results obtained there. All the theoretical results are tested against the numerical results showing excellent qualitative and good quantitative agreement.
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影响因子：
3
作者：
L. Segel
通讯作者：
L. Segel
影响因子：
1.4
作者：
Ma, Manjun;Hu, Jiajia;Tao, Jicheng;Tong, Changqing
通讯作者：
Tong, Changqing
影响因子：
2
作者：
KELLER, EF;SEGEL, LA
通讯作者：
SEGEL, LA
细胞增殖的广义体积填充趋化模型的模式
影响因子：
2.2
作者：
Manjun Ma;Zhian Wang
通讯作者：
Zhian Wang
DOI：
10.1007/bf02476407
发表时间：
1953-01-01
期刊：
BULL MATH BIOPHYS
影响因子：
--
作者：
PATLAK, CLIFFORD S.
通讯作者：
PATLAK, CLIFFORD S.