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Journal of Mathematical Biology

, Volume 75, Issue 5, pp 1047–1073 | Cite as

Wavenumber selection in coupled transport equations

  • Arnd ScheelEmail author
  • Angela Stevens
Article

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.

Keywords

Traveling wave Standing wave Balance laws Coupled transport equations Invasion fronts Wavenumber selection 

Mathematics Subject Classification

24B36 92C15 

Notes

Acknowledgements

A. Scheel was partially supported through NSF grants DMS-1612441 and DMS-1311740, through a DAAD Faculty Research Visit Grant, WWU Fellowship, and a Humboldt Research Award. A. Stevens was partially supported by the DFG Excellence Cluster Cells in Motion (CiM). A. Scheel gratefully acknowledges generous hospitality during his extended research stay at the WWU Münster.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.School of MathematicsUniversity of MinnesotaMinneapolisUSA
  2. 2.Fachbereich Mathematik und InformatikUniversität MünsterMünsterGermany

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