Keywords
markov process, cell motion, interevent time
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.
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.
https://scholarsarchive.byu.edu/facpub/2721
Document Type
Peer-Reviewed Article
Publication Date
2017
Permanent URL
http://hdl.lib.byu.edu/1877/5547
Publisher
Springer
Language
English
College
Physical and Mathematical Sciences
Department
Mathematics
Copyright Status
Springer. This is the author's submitted version of this article.
Copyright Use Information
http://lib.byu.edu/about/copyright/
