Stability of constant steady states of an attraction-repulsion chemotaxis system

TL;DR

This paper investigates the stability conditions of constant steady states in an attraction-repulsion chemotaxis system, highlighting differences between attraction and repulsion dynamics and establishing criteria for stability.

Contribution

It provides a new condition under which the attraction-repulsion chemotaxis system exhibits stable constant steady states, extending understanding of stability in such systems.

Findings

In attraction chemotaxis, stability depends on specific regions.

In repulsion chemotaxis, all positive steady states are stable.

A new stability condition for the combined attraction-repulsion system.

Abstract

The Cauchy problem for the attraction-repulsion chemotaxis system in the whole $n$-dimensional space has uncountable constant steady states. In the attraction chemotaxis system, each positive constant steady state is stable if it is in a certain region. On the other hand, in the repulsion chemotaxis system, every positive constant steady state is stable. Our main purpose of this paper is to give a suitable condition under which the attraction-repulsion chemotaxis system has also stable constant steady states.