The aim of the article is to study the stability of a non-local kinetic model proposed in [17], that is a kinetic model for cell migration taking into account the non-local sensing performed by a cell in order to decide its direction and speed of movement. 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 to the case of different mean speeds in different directions.

中文翻译：

---

具有密度依赖性方向偏差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[[]中提出的非局部动力学模型的稳定性。17这是一种细胞迁移的动力学模型，考虑了细胞执行的非局部感测以确定其移动方向和速度。我们表明，图案形成是由于调制一个无量纲参数而产生的，该参数取决于翻转频率，感应半径，给定方向上的平均速度，均匀的构型密度和对细胞密度的战术响应。数值模拟表明，我们的线性稳定性分析非常准确地预测了确定不稳定性和图案形成的参数范围。我们还将稳定性分析扩展到在不同方向上具有不同平均速度的情况。