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

Ni, Wenjie; Shi, Junping; Wang, Mingxin

doi:10.1090/proc/15370

Global stability of spatially nonhomogeneous steady state solution in a diffusive Holling-Tanner predator-prey model
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by Wenjie Ni, Junping Shi and Mingxin Wang PDF

Proc. Amer. Math. Soc. 149 (2021), 3781-3794 Request permission

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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