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

被引：24

作者：

Bengfort, Michael ^{[1
]}

Malchow, Horst ^{[1
]}

Hilker, Frank M. ^{[1
]}

机构：

[1] Univ Osnabruck, Inst Environm Syst Res, Sch Math Comp Sci, Barbarastr 12, D-49076 Osnabruck, Germany

来源：

JOURNAL OF MATHEMATICAL BIOLOGY | 2016年 / 73卷 / 03期

关键词：

Ecological diffusion; Spatial inhomogeneities; Pattern formation; Speed of invasion; Reaction-diffusion equations; Plankton blooms; Turing patterns; Movement behavior; RANDOM-WALK MODELS; FICKS LAW; PLANKTON; DYNAMICS; PHYTOPLANKTON; TRAJECTORIES; ZOOPLANKTON; INVASION; SPREAD; SCALES;

D O I：

10.1007/s00285-016-0966-8

中图分类号：

Q [生物科学];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

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.

引用

页码：683 / 704

页数：22

共 57 条

[41] Fick's law and Fokker-Planck equation in inhomogeneous environments [J].