Dynamics of a predator-prey system in open advective heterogeneous environments

TL;DR

This paper studies how dispersal, advection, and environmental heterogeneity influence predator-prey dynamics, extending previous models by analyzing stability conditions in more complex, open, advective environments.

Contribution

It advances understanding of predator-prey interactions by incorporating advection and heterogeneity, addressing an open problem and generalizing prior models.

Findings

Stability depends on dispersal, mortality, and advection rates.

Heterogeneity complicates the stability analysis compared to homogeneous models.

Provides a generalized framework for predator-prey dynamics in advective environments.

Abstract

In this paper, we investigate the effect of dispersal and advection on the dynamics of a predator-prey model. More precisely, we show that the linear stability of the semi-trivial steady state is determined by the dispersal rate, the mortality rate of the predator and the advection rate. We point out that compared to homogeneous intrinsic growth rate and carrying capacity, the case in this paper is more complicated. This work gives a investigation to an open problem proposed by Nie et al. in \cite{NWW} by considering a more general model, and then, can be seen as a further development of their work \cite{NWW}.