Global phase diagrams of run-and-tumble dynamics: equidistribution, waves, and blowup
arXiv:1805.11903 · doi:10.1088/1361-6544/ab046d
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.
14 pages, 3 figures