markov process, cell motion, interevent time
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.
Original Publication Citation
Journal of Mathematical Biology 74:727-753 (2017) doi:10.1007/s00285-016-1040-2
BYU ScholarsArchive Citation
Dallon, J. C.; Despain, L C.; Evans, E J.; Grant, C P.; and Smith, Willaim V., "A continuous time model of centrally controlled motion with random switching terms" (2017). Faculty Publications. 2721.
Physical and Mathematical Sciences
Springer. This is the author's submitted version of this article.
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