The aim of this article is to study the stability of a non-local kinetic model proposed by Loy & Preziosi (2020a) in which the cell speed is affected by the cell population density non-locally measured and weighted according to a sensing kernel in the direction of polarization and motion. We perform the analysis in a |$d$|-dimensional setting. We study the dispersion relation in the one-dimensional case and we show that the stability depends on two dimensionless parameters: the first one represents the stiffness of the system related to the cell turning rate, to the mean speed at equilibrium and to the sensing radius, while the second one relates to the derivative of the mean speed with respect to the density evaluated at the equilibrium. It is proved that for Dirac delta sensing kernels centered at a finite distance, corresponding to sensing limited to a given distance from the cell center, the homogeneous configuration is linearly unstable to short waves. On the other hand, for a uniform sensing kernel, corresponding to uniformly weighting the information collected up to a given distance, the most unstable wavelength is identified and consistently matches the numerical solution of the kinetic equation.

中文翻译：

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具有密度依赖性速度的细胞迁移的非局部动力学模型的稳定性

本文的目的是研究由提出的非局部动力学模型的稳定性 Loy & Preziosi (2020a)，其中细胞速度受细胞群密度的影响，根据极化和运动方向的传感内核非局部测量和加权。我们在|$d$| 中执行分析-维度设置。我们研究了一维情况下的色散关系，我们表明稳定性取决于两个无量纲参数：第一个代表与细胞转动速率、平衡时的平均速度和传感半径相关的系统刚度，而第二个涉及平均速度相对于平衡时评估的密度的导数。已证明，对于以有限距离为中心的 Dirac delta 传感内核，对应于距离单元中心给定距离的传感，均匀配置对短波是线性不稳定的。另一方面，对于统一的感知内核，对应于统一加权收集到给定距离的信息，