Global phase diagrams of run-and-tumble dynamics

Equidistribution, waves, and blowup

Kyungkeun Kang, Arnd Scheel, Angela Stevens

Research output: Contribution to journalArticle

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.

Original languageEnglish
Pages (from-to)2128-2146
Number of pages19
JournalNonlinearity
Volume32
Issue number6
DOIs
Publication statusPublished - 2019 May 8

Fingerprint

Equidistribution
Blow-up
Phase Diagram
Phase diagrams
phase diagrams
Barreling
Critical Dynamics
Finite Time Blow-up
Mass Conservation
Blow-up of Solutions
Ripple
Phase boundaries
ripples
conservation
Conservation
counters
Decay
decay

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

Cite this

Kang, Kyungkeun ; Scheel, Arnd ; Stevens, Angela. / Global phase diagrams of run-and-tumble dynamics : Equidistribution, waves, and blowup. In: Nonlinearity. 2019 ; Vol. 32, No. 6. pp. 2128-2146.
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Global phase diagrams of run-and-tumble dynamics : Equidistribution, waves, and blowup. / Kang, Kyungkeun; Scheel, Arnd; Stevens, Angela.

In: Nonlinearity, Vol. 32, No. 6, 08.05.2019, p. 2128-2146.

Research output: Contribution to journalArticle

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