title: The Fokker-Planck law of diffusion and pattern formation in heterogeneous environments.
abstract: 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.
authors.affiliation: Institute of Environmental Systems Research, School of Mathematics/Computer Science, Osnabrück University, Barbarastr. 12, 49076, Osnabrück, Germany. mbengfort@uni-osnabrueck.de.
authors.forename: Michael
authors.initials: M
authors.lastname: Bengfort
authors.affiliation: Institute of Environmental Systems Research, School of Mathematics/Computer Science, Osnabrück University, Barbarastr. 12, 49076, Osnabrück, Germany.
authors.forename: Horst
authors.initials: H
authors.lastname: Malchow
authors.affiliation: Institute of Environmental Systems Research, School of Mathematics/Computer Science, Osnabrück University, Barbarastr. 12, 49076, Osnabrück, Germany.
authors.forename: Frank M
authors.initials: FM
authors.lastname: Hilker
mesh_terms: D004777:Environment; D020387:Food Chain; D008954:Models, Biological; D008956:Models, Chemical
keywords: Ecological diffusion; Movement behavior; Pattern formation; Plankton blooms; Reaction–diffusion equations; Spatial inhomogeneities; Speed of invasion; Turing patterns