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Published on: September 26, 2016
The Fokker-Planck law of diffusion and pattern formation in heterogeneous environments
Michael Bengfort1, Horst Malchow2, Frank M Hilker2
1Institute of Environmental Systems Research, School of Mathematics/Computer Science, Osnabrück University, Barbarastr. 12, 49076, Osnabrück, Germany. mbengfort@uni-osnabrueck.de.
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.
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