High multiplicity and global structure of coexistence states in a predator-prey model with saturation

TL;DR

This study demonstrates that a predator-prey model with saturation can exhibit an arbitrarily large number of coexistence states and explores the global structure of these states as saturation increases.

Contribution

It reveals the potential for unlimited coexistence states in a predator-prey system with saturation and characterizes their global structure at high saturation levels.

Findings

Number of coexistence states can be arbitrarily large.

Global structure of coexistence states is characterized at high saturation.

Model parameters influence the multiplicity of coexistence states.

Abstract

This paper establishes that, under the appropriate range of values of the parameters involved in the formulation of the model, a diffusive predator-prey system with saturation can have an arbitrarily large number of coexistence states for sufficiently large saturation rates. Moreover, it ascertains the global structure of the set of coexistence states in the limiting system as the saturation rate blows-up.