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

作者：Dallon J C; Despain Lynnae C; Evans Emily J; Grant Christopher P; Smith W V

来源：Journal of Mathematical Biology, 2017, 74(3): 727-753.

DOI：10.1007/s00285-016-1040-2

• Random switching
• Differential equations
• Markov process

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.

• 出版日期2017-2