具有随机切换的中心协调运动的连续时间模型
A continuous-time model of centrally coordinated motion with random switching
摘要：
本文考虑随机切换的微分问题，具体应用到细胞的运动和集中协调运动。从先前提出的细胞运动的微分方程模型开始，我们将弛豫时间设置为零，并考虑得到的更简单的模型。我们证明了这个模型是适定的，在这个意义上，它对应于一个纯跳跃型连续时间马尔可夫过程（没有爆炸）。然后，我们描述了模型的长期行为，首先指定一个吸引的稳态分布的模型的投影，然后通过检查细胞中心的预期位置时，初始数据是兼容的稳定状态。在此条件下，我们给出了期望速度的计算公式，并对该公式的有效性给出了严格的证明。最后，我们将这些理论结果与数值模拟的结果进行了比较。
英文摘要：
This paper considers differential problems with random switching, with specific applications to the motion of cells and centrally coordinated motion. Starting with a differential-equation model of cell motion that was proposed previously, we set the relaxation time to zero and consider the simpler model that results. We prove that this model is well-posed, in the sense that it corresponds to a pure jump-type continuous-time Markov process (without explosion).We then describe the model's long-time behavior, first by specifying an attracting steady-state distribution for a projection of the model, then by examining the expected location of the cell center when the initial data is compatible with that steady-state. Under such conditions, we present a formula for the expected velocity and give a rigorous proof of that formula's validity. We conclude the paper with a comparison between these theoretical results and the results of numerical simulations.
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