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

Kyungkeun Kang; Arnd Scheel; Angela Stevens

doi:10.1088/1361-6544/ab046d

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arXiv · 1805.11903

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

Kyungkeun Kang·Arnd Scheel·Angela Stevens

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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.

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Kyungkeun Kang, Arnd Scheel, Angela Stevens. 2018-05-30. Global phase diagrams of run-and-tumble dynamics: equidistribution, waves, and blowup. https://doi.org/10.1088/1361-6544%2Fab046d

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