Spreading speeds along shifting resource gradients in reaction-diffusion models and lattice differential equations.

reaction-diffusion model;lotka-volterra competition model;lattice differential equations;spreading speed;traveling wave;upper and lower solutions

Jin Shang

University:University of Louisville

Department:Mathematics

关键词: reaction-diffusion model;    lotka-volterra competition model;    lattice differential equations;    spreading speed;    traveling wave;    upper and lower solutions;   

Others  :  https://ir.library.louisville.edu/cgi/viewcontent.cgi?article=3666&context=etd

美国|英语

来源: The Universite of Louisville's Institutional Repository

【 摘 要 】

A reaction-diffusion model and a lattice differential equation are introduced to describe the persistence and spread of a species along a shifting habitat gradient. The species is assumed to grow everywhere in space and its growth rate is assumed to be monotone and positive along the habitat region. We show that the persistence and spreading dynamics of a species are dependent on the speed of the shifting edge of the favorable habitat, c, as well as c*(∞) and c*(−∞), which are formulated in terms of the dispersal kernel and species growth rates in both directions. When the favorable habitat edge shifts towards the right, c>0, we demonstrate that the rightward spreading speed is c*(∞) when c is relatively small and is c*(−∞) when c is relatively large, and the leftward spreading speed is c*(−∞). When the favorable habitat edge shifts towards the left, c*(∞), and the leftward spreading speed is one of |c|, c*(−∞) or c*(∞). We also show the persistence and spreading dynamics of two competing species along shifting habitats in the simplest situations. Their spreading behavior will be affected by the resource distribution and habitat shifting speed.