具有密度依赖取向偏差的细胞迁移非局部动力学模型的稳定性
Stability of a non-local kinetic model for cell migration with density dependent orientation bias
摘要：
本文的目的是研究Loy和Preziosi（2019 a）提出的非局部动力学模型的稳定性。我们将总体分为两个亚组，并进行线性稳定性分析。我们表明，图案形成的结果从一个无量纲的参数，取决于翻滚频率，传感半径，在一个给定的方向上的平均速度，均匀的配置密度和细胞密度的战术响应调制。数值模拟表明，我们的线性稳定性分析预测相当精确的参数范围内确定不稳定性和图案的形成。我们还扩展了在不同方向上不同平均速度的情况下的稳定性分析。在这种情况下，对于导致不稳定性的参数值，会产生行波图案。
英文摘要：
The aim of the article is to study the stability of a non-local kinetic model proposed by Loy and Preziosi (2019a). We split the population in two subgroups and perform a linear stability analysis. We show that pattern formation results from modulation of one non-dimensional parameter that depends on the tumbling frequency, the sensing radius, the mean speed in a given direction, the uniform configuration density and the tactic response to the cell density. Numerical simulations show that our linear stability analysis predicts quite precisely the ranges of parameters determining instability and pattern formation. We also extend the stability analysis in the case of different mean speeds in different directions. In this case, for parameter values leading to instability travelling wave patterns develop.
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