Preprint 38/2018

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

Kyungkeun Kang, Arnd Scheel, and Angela Stevens

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Submission date: 30. May. 2018
Pages: 16
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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.

08.06.2018, 00:13