Dynamics of a diffusive predator-prey model: the effect of conversion rate

TL;DR

This paper analyzes a diffusive predator-prey model, demonstrating how the conversion rate influences the stability of equilibria and the potential for pattern formation, with implications for ecological dynamics.

Contribution

It provides new theoretical results on the global attractivity of equilibria and conditions preventing pattern formation based on the conversion rate.

Findings

Small conversion rate ensures global stability of constant equilibria.

Large conversion rate prevents the existence of non-constant steady states.

Parameter ranges identified where complex patterns cannot form.

Abstract

A general diffusive predator-prey model is investigated in this paper. We prove the global attractivity of constant equilibria when the conversion rate is small, and the non-existence of non-constant positive steady states when the conversion rate is large. The results are applied to several predator-prey models and give some ranges of parameters where complex pattern formation cannot occur.