The Fokker-Planck law of diffusion and pattern formation in heterogeneous environments

Autor(en): Bengfort, Michael 
Malchow, Horst 
Hilker, Frank M.
Stichwörter: Biology; DYNAMICS; Ecological diffusion; FICKS LAW; INVASION; Life Sciences & Biomedicine - Other Topics; Mathematical & Computational Biology; Movement behavior; Pattern formation; PHYTOPLANKTON; PLANKTON; Plankton blooms; RANDOM-WALK MODELS; Reaction-diffusion equations; SCALES; Spatial inhomogeneities; Speed of invasion; SPREAD; TRAJECTORIES; Turing patterns; ZOOPLANKTON
Erscheinungsdatum: 2016
Herausgeber: SPRINGER HEIDELBERG
Journal: JOURNAL OF MATHEMATICAL BIOLOGY
Volumen: 73
Ausgabe: 3
Startseite: 683
Seitenende: 704
Zusammenfassung: 
We analyze the influence of spatially inhomogeneous diffusion on several common ecological problems. Diffusion is modeled with Fick's law and the Fokker-Planck law of diffusion. We discuss the differences between the two formalisms and when to use either the one or the other. In doing so, we start with a pure diffusion equation, then turn to a reaction-diffusion system with one logistically growing component which invades the spatial domain. We also look at systems of two reacting components, namely a trimolecular oscillating chemical model system and an excitable predator-prey model. Contrary to Fickian diffusion, spatial inhomogeneities promote spatial and spatiotemporal pattern formation in case of Fokker-Planck diffusion.
ISSN: 03036812
DOI: 10.1007/s00285-016-0966-8

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