Global stability of spatially nonhomogeneous steady state solution in a diffusive Holling-Tanner predator-prey model

2020/07/29 by Wenjie Ni, Ni, Wenjie, Junping Shi +3
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · Social Sciences · #Evolution and Genetic Dynamics #Evolutionary Game Theory and Cooperation #Mathematical and Theoretical Epidemiology and Ecology Models #math.AP #msc:35B35 #msc:35B40 #msc:35K51 #msc:92D25

paper · pdf · doi:10.48550/arxiv.2007.15056

14 pages

arxiv created 2020/07/29 · arxiv updated 2020/07/31

Abstract

The global stability of the nonhomogeneous positive steady state solution to a diffusive Holling-Tanner predator-prey model in a heterogeneous environment is proved by using a newly constructed Lyapunov function and estimates of nonconstant steady state solutions. The techniques developed here can be adapted for other spatially heterogeneous consumer-resource models.

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