Phys. Rev. E 96, 022220 (2017) - Fragility of reaction-diffusion models with respect to competing advective processes

Fragility of reaction-diffusion models with respect to competing advective processes

Oleg Kogan, Kevin O'Keeffe, and Christopher R. Myers

Phys. Rev. E 96, 022220 – Published 29 August 2017

Abstract

We study the coupling of a Fisher-Kolmogorov-Petrovsky-Piskunov (FKPP) equation to a separate, advection-only transport process. We find that an infinitesimal coupling can cause a finite change in the speed and shape of the reaction front, indicating the fragility of the FKPP model with respect to such a perturbation. The front dynamics can be mapped to an effective FKPP equation only at sufficiently fast diffusion or large coupling strength. We also discover conditions when the front width diverges and when its speed is insensitive to the coupling. At zero diffusion in our mean-field description, the downwind front speed goes to a finite value as the coupling goes to zero.

Received 8 April 2016
Revised 26 May 2017

DOI:https://doi.org/10.1103/PhysRevE.96.022220

©2017 American Physical Society

Physics Subject Headings (PhySH)

Biological fluid dynamics Chemical kinetics, dynamics & catalysis Ecological pattern formation Plant ecology Population dynamics Transport phenomena

Front propagation Nonlinear waves Reaction diffusion systems

Nonlinear Dynamics

Authors & Affiliations

Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853, USA

Center for Applied Mathematics, Cornell University, Ithaca, New York 14853, USA

Christopher R. Myers

Laboratory of Atomic and Solid State Physics, and Institute of Biotechnology, Cornell University, Ithaca, New York 14853, USA

^*obk5@cornell.edu

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Issue

Vol. 96, Iss. 2 — August 2017

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