Global phase diagrams of run-and-tumble dynamics: equidistribution, waves, and blowup

Kyungkeun Kang, Arnd Scheel, and Angela Stevens

Contact the author: Please use for correspondence this email.
Submission date: 30. May. 2018
Pages: 16
published in: Nonlinearity, 32 (2019) 6, p. 2128-2146 
DOI number (of the published article): 10.1088/1361-6544/ab046d
Bibtex
Download full preprint: PDF (1537 kB)

Abstract:
For spatially one-dimensional run-and-tumble dynamics with mass conservation we develop a coarse phase diagram, that discriminates between global decay to equidistributed constant states, existence of spatially non-trivial waves, and finite time blowup of solutions. Motivated by counter-migrating ripples of high and low population density and fruiting body formation in myxobacteria, we identify phase boundaries as particular critical tumbling dynamics that allow for switching between these spatio-temporal phases upon slight changes in mass densities or parameter values.