MiS Preprint Repository

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MiS Preprint

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

Kyungkeun Kang, Arnd Scheel and Angela Stevens


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.

May 30, 2018
Jun 4, 2018

Related publications

2019 Repository Open Access
Kyungkeun Kang, Arnd Scheel and Angela Stevens

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

In: Nonlinearity, 32 (2019) 6, pp. 2128-2146