# Improvement of conditions for asymptotic stability in a two-species chemotaxis-competition model with signal-dependent sensitivity

## TL;DR

This paper improves the mathematical conditions required for ensuring the long-term stability of a two-species chemotaxis-competition system with signal-dependent sensitivity, advancing understanding of such biological models.

## Contribution

It refines the existing conditions for asymptotic stability in a chemotaxis-competition model, narrowing the gap between previous theoretical results.

## Key findings

- Enhanced conditions for asymptotic stability are established.
- The results extend previous stability criteria.
- The work provides a more comprehensive understanding of the model's behavior.

## Abstract

This paper deals with the two-species chemotaxis-competition system. About the problem, Bai--Winkler first obtained asymptotic stability under some conditions. Recently, the conditions assumed in the previous work were improved; however, there is a gap between the conditions assumed in the previous works. The purpose of this work is to improve the conditions assumed in the previous works for asymptotic behavior.