集体细胞迁移模型中极化和去极化行波解的分类与稳定性分析
Classification and stability analysis of polarising and depolarising travelling wave solutions for a model of collective cell migration
AI总结：
本研究对集体细胞迁移一维模型的行波解进行分类，识别出四种极化和去极化波，并利用谱理论和Evans函数数值与解析结合地分析其线性稳定性。
摘要：
我们研究了一个一维连续统模型的行波解，该模型用于描述集体细胞迁移，其中细胞以位置和极性为特征。我们识别出四种不同类型的行波解，它们代表由碰撞或分离的细胞片产生的极化和去极化波，正如在模型伤口实验中所观察到的那样。我们通过数值方法和谱理论研究了行波解的线性稳定性。这涉及Evans函数的计算，其中大部分我们可以显式地进行，最后一步留给数值模拟。
英文摘要：
We study travelling wave solutions of a 1D continuum model for collective cell migration in which cells are characterised by position and polarity. Four different types of travelling wave solutions are identified which represent polarisation and depolarisation waves resulting from either colliding or departing cell sheets as observed in model wound experiments. We study the linear stability of the travelling wave solutions numerically and using spectral theory. This involves the computation of the Evans function most of which we are able to carry out explicitly, with one final step left to numerical simulation.
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