Some remarks on segregation of k species in strongly competing system

2021/03/11 by Flavia Lanzara, Eugenio Montefusco, Lanzara, Flavia +1
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · #35J47 #Analysis of PDEs (math.AP) #Evolution and Genetic Dynamics #FOS: Mathematics #Mathematical Biology Tumor Growth #Mathematical and Theoretical Epidemiology and Ecology Models #Primary 35Bxx #Secondary 92D25

paper · pdf · doi:10.48550/arxiv.2103.06808

openalex publication_date 2021/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Spatial segregation occurs in population dynamics when k species interact in a highly competitive way. As a model for the study of this phenomenon, we consider the competition-diffusion system of k differential equations -Δu_i(x)=-μu_i (x)∑_{j≠ i} u_j (x) i=1,...,k in a domain D with appropriate boundary conditions. Any u_i represents a population density and the parameter μ determines the interaction strength between the populations. The purpose of this paper is to study the geometry of the limiting configuration as μ\longrightarrow+∞ on a planar domain for any number of species. If k is even we show that some limiting configurations are strictly connected to the solution of a Dirichlet problem for the Laplace equation.

Citations

• Dynamics of strongly competing systems with many species

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