Growth and dispersal with inertia: Hyperbolic reaction-transport systems

Vicenç Méndez, Daniel Campos, Werner Horsthemke

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Abstract

© 2014 American Physical Society. We investigate the behavior of five hyperbolic reaction-diffusion equations most commonly employed to describe systems of interacting organisms or reacting particles where dispersal displays inertia. We first discuss the macroscopic or mesoscopic foundation, or lack thereof, of these reaction-transport equations. This is followed by an analysis of the temporal evolution of spatially uniform states. In particular, we determine the uniform steady states of the reaction-transport systems and their stability properties. We then address the spatiotemporal behavior of pure death processes. We end with a unified treatment of the front speed for hyperbolic reaction-diffusion equations with Kolmogorov-Petrosvskii-Piskunov kinetics. In particular, we obtain an exact expression for the front speed of a general class of reaction correlated random walk systems. Our results establish that three out of the five hyperbolic reaction-transport equations provide physically acceptable models of biological and chemical systems.
Original languageEnglish
Article number042114
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume90
DOIs
Publication statusPublished - 7 Oct 2014

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    Méndez, V., Campos, D., & Horsthemke, W. (2014). Growth and dispersal with inertia: Hyperbolic reaction-transport systems. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 90, [042114]. https://doi.org/10.1103/PhysRevE.90.042114