Abstract
We study mechanisms for wavenumber selection in a minimal model for run-and-tumble dynamics. We show that nonlinearity in tumbling rates induces the existence of a plethora of traveling- and standing-wave patterns, as well as a subtle selection mechanism for the wavenumbers of spatio-temporally periodic waves. We comment on possible implications for rippling patterns observed in colonies of myxobacteria.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1047-1073 |
| Number of pages | 27 |
| Journal | Journal of Mathematical Biology |
| Volume | 75 |
| Issue number | 5 |
| DOIs | |
| State | Published - Nov 1 2017 |
Bibliographical note
Publisher Copyright:© 2017, Springer-Verlag Berlin Heidelberg.
Keywords
- Balance laws
- Coupled transport equations
- Invasion fronts
- Standing wave
- Traveling wave
- Wavenumber selection
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