A continuous-time model of centrally coordinated motion with random switching

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• 作者：J. C. Dallon ; Lynnae C. Despain ; Emily J. Evans…
• 关键词：Random switching ; Differential equations ; Markov process
• 刊名：Journal of Mathematical Biology
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：74
• 期：3
• 页码：727-753
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematical and Computational Biology; Applications of Mathematics;
• 出版者：Springer Berlin Heidelberg
• ISSN：1432-1416
• 卷排序：74

文摘

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.