Manhart, A;
(2019)
Counter-propagating wave patterns in a swarm model with memory.
Journal of Mathematical Biology
, 78
(3)
pp. 655-682.
10.1007/s00285-018-1287-x.
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Abstract
Hyperbolic transport-reaction equations are abundant in the description of movement of motile organisms. Here, we focus on a system of four coupled transport-reaction equations that arises from an age-structuring of a species of turning individuals. By modeling how the behavior depends on the time since the last reversal, we introduce a memory effect. The highlight consists of the explicit construction and characterization of counter-propagating traveling waves, patterns which have been observed in bacterial colonies. Stability analysis reveals conditions for the wave formation as well as pulsating-in-time spatially constant solutions.
| Type: | Article |
|---|---|
| Title: | Counter-propagating wave patterns in a swarm model with memory |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s00285-018-1287-x |
| Publisher version: | https://doi.org/10.1007/s00285-018-1287-x |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | traveling waves, hyperbolic equations, viscous limit, myxobacteria, wave formation, age-structured equations, pattern formation |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10085914 |
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