Global existence and stabilization in a forager-exploiter model with general logistic sources

TL;DR

This paper establishes conditions for the global existence and boundedness of solutions in a forager-exploiter model with logistic sources, analyzing long-term behavior under nutrient supply assumptions.

Contribution

It introduces a new boundedness criterion and proves global existence for high-dimensional cases with specific logistic degradation conditions.

Findings

Solutions remain bounded globally under certain conditions.

Long-term behavior depends on nutrient supply properties.

The model extends understanding of forager-exploiter dynamics.

Abstract

We study a forager-exploiter model with generalized logistic sources in a smooth bounded domain with homogeneous Neumann boundary conditions. A new boundedness criterion is developed to prove the global existence and boundedness of the solution. Under some conditions on the logistic degradation rates, the classical solution exists globally and remain bounded in the high dimensions. Moreover, the large time behavior of the obtained solution is investigated in the case of the nutrient supply is a positive constant or has fast decaying property.