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

TL;DR

This paper proves the global stability of a nonhomogeneous steady state in a spatial predator-prey model using a novel Lyapunov function, with methods applicable to other heterogeneous ecological models.

Contribution

It introduces a new Lyapunov function approach to establish global stability in a spatially heterogeneous predator-prey system.

Findings

Proved global stability of nonhomogeneous steady states.

Developed a new Lyapunov function method.

Applicable to other spatially heterogeneous models.

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.