Attractivity and stability in the competitive systems of PDEs of Kolmogorov type

TL;DR

This paper establishes conditions under which multi-species competitive PDE systems of Kolmogorov type are guaranteed to be uniformly stable and globally attractive, enhancing understanding of their long-term behavior.

Contribution

It provides a new sufficient condition for stability and attractivity in nonautonomous multi-species PDE systems of Kolmogorov type under Neumann boundary conditions.

Findings

System is uniformly stable under the given condition.

System is globally attractive under the given condition.

Results apply to nonautonomous multi-species PDEs of Kolmogorov type.

Abstract

We consider $N$-species nonautonomous competitive systems of partial differential equations of Kolmogorov type. Under the Neumann boundary conditions we give a sufficient condition for the system to be uniformly stable and globally attractive.