Multi-spots Steady States in Two-species Keller-Segel Models with Logistic Growth: Large Chemotactic Attraction Regime

TL;DR

This paper constructs multi-spot steady states in a two-species chemotaxis model with logistic growth under strong chemotactic attraction, revealing how cellular densities form localized aggregations influenced by Green's functions.

Contribution

It introduces a novel inner-outer gluing method to analyze multi-spot steady states in two-species chemotaxis systems with logistic growth, extending understanding beyond single-species models.

Findings

Existence of multi-spot steady states under large chemo-attractive coefficients.

Connection of cellular density profiles with solutions to Liouville systems.

Locations of spots determined by reduced-wave Green's functions.

Abstract

One of the most important findings in the study of chemotactic process is self-organized cellular aggregation, and a high volume of results are devoted to the analysis of a concentration of single species. Whereas, the multi-species case is not understood as well as the single species one. In this paper, we consider two-species chemotaxis systems with logistic source in a bounded domain $\Omega\subset \mathbb R^2.$ Under the large chemo-attractive coefficients and one certain type of chemical production coefficient matrices, we employ the inner-outer gluing approach to construct multi-spots steady states, in which the profiles of cellular densities have strong connections with the entire solutions to Liouville systems and their locations are determined in terms of reduced-wave Green's functions. In particular, some numerical simulations and formal analysis are performed to support our rigorous studies.