Positive Solutions of Competition Model with Saturation

TL;DR

This paper investigates positive solutions of a diffusive competition model with saturation, analyzing stability, multiplicity, and bifurcation of coexistence states using topological degree theory.

Contribution

It introduces new results on the existence, stability, and bifurcation of positive solutions in a saturation competition model, employing topological degree methods.

Findings

At least two positive solutions exist under certain conditions.

Stability and multiplicity of coexistence states are characterized.

Bifurcation analysis reveals instability and multiple coexistence states.

Abstract

In this paper, the positive solutions of a diffusive competition model with saturation are mainly discussed. Under certain conditions, the stability and multiplicities of coexistence states are analyzed. And by using the topological degree theory in cones, it is proved that the problem has at least two positive solutions under certain conditions. Finally, investigating the bifurcation of coexistence states emanating from the semi-trivial solutions, some instability and multiplicity results of coexistence state are expressed.