More than Skew: Asymmetric Wave Propagation in a Reaction-Diffusion-Convection System

Authors

  • Edward H. Flach Integrated Mathematical Oncology, Moffitt Cancer Center and Research Institute
  • John Norbury Mathematical Institute, University of Oxford
  • Santiago Schnell Department of Molecular & Integrative Physiology, Department of Computational Medicine & Bioinformatics, Brehm Center for Diabetes Research, University of Michigan Medical School

DOI:

https://doi.org/10.11145/j.biomath.2013.03.027

Keywords:

reaction-diffusion, convection, limit cycle, Schnakenberg, travelling wave

Abstract

Convection-induced instability in reaction-diffusion systems produces complicated patterns of oscillations behind propagating wavefronts. We transform the system twice: into lambda-omega form, then into polar variables. We find analytical estimates for the wavefront speed which we confirm numerically.Our previous work examined a simpler system [E. H. Flach, S. Schnell, and J. Norbury, Phys. Rev. E 76, 036216 (2007)]; the onset of instability is qualitatively different В in numerical solutions of this system. We modify our estimates and connect the two different behaviours. Our estimate explains how the Turing instability fits with pattern found in reaction-diffusion-convection systems. Our results can have important applications to the pattern formation analysis of biological systems.

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Published

2013-03-09

Issue

Vol. 2 No. 1 (2013)

Section

Original Articles

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