Bifurcation of finger-like structures in traveling waves of epithelial tissues spreading
Bifurcation of finger-like structures in traveling waves of epithelial tissues spreading
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DOI：
10.1016/j.jmaa.2024.128338
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发表时间：
2023-11
影响因子：
1.3
通讯作者：
L. Berlyand;Antonina Rybalko;V. Rybalko;C. A. Safsten
中科院分区：
文献类型：
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作者：
L. Berlyand;Antonina Rybalko;V. Rybalko;C. A. Safsten
我们考虑了由R。阿勒特角Blanch-Mercader和J. Casademunt，2019年。相应的自由边界问题具有平坦波前行波解。在周期扰动下，这些解决方案的线性稳定性。它示出的解决方案是稳定的短波扰动，而表现出长波不稳定性在一定条件下的模型参数（如果牵引力足够强）。然后，考虑指定的周期作为分歧参数，我们建立了出现的非平凡行波解的指状周期结构（图案）。我们还构造了解在分歧点附近的渐近展开式，并研究了它们的稳定性。我们表明，根据收缩系数的值，分叉可以是一个亚临界或超临界的干草叉。
We consider a continuous active polar fluid model for the spreading of epithelial monolayers introduced by R. Alert, C. Blanch-Mercader, and J. Casademunt, 2019. The corresponding free boundary problem possesses flat front traveling wave solutions. Linear stability of these solutions under periodic perturbations is considered. It is shown that the solutions are stable for short-wave perturbations while exhibiting long-wave instability under certain conditions on the model parameters (if the traction force is sufficiently strong). Then, considering the prescribed period as the bifurcation parameter, we establish the emergence of nontrivial traveling wave solutions with a finger-like periodic structure (pattern). We also construct asymptotic expansions of the solutions in the vicinity of the bifurcation point and study their stability. We show that, depending on the value of the contractility coefficient, the bifurcation can be a subcritical or a supercritical pitchfork.