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arXiv · 1507.04787

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

John C. Dallon·Lynnae C. Despain·Emily J. Evans·Christopher P. Grant·William V. Smith
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Abstract

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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John C. Dallon, Lynnae C. Despain, Emily J. Evans, Christopher P. Grant, William V. Smith. 2015-07-16. A continuous-time model of centrally coordinated motion with random switching. https://arxiv.org/abs/1507.04787

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