Minimal coexistence configurations for multispecies systems

Coexistence and Segregation for Strongly Competing Species in Special Domains

We deal with strongly competing multispecies systems of Lotka-Volterra type with homogeneous Dirichlet boundary conditions. For a class of nonconvex domains composed by balls connected with thin corridors, we show the occurrence of pattern formation (coexistence and spatial segregation of all the species), as the competition grows indefinitely. As a result we prove the existence and uniqueness of solutions for a remarkable system of differential inequalities involved in segregation phenomena and optimal partition problems.

Global minimizers of coexistence for competing species

A class of variational models describing ecological systems of k species competing for the same resources is investigated. The occurrence of coexistence in minimal energy solutions is discussed and positive results are proven for suitably differentiated internal dynamics.

两物种Lotka-Volterra竞争-扩散系统行波的存在性与渐近稳定性：几何奇异摄动方法

Existence and Asymptotic Stability of Traveling Waves of Two-species Lotka-Volterra Competition-Diffusion Systems via Geometric Singular Perturbations

本文通过几何奇异摄动理论，证明了两物种Lotka-Volterra竞争-扩散系统中连接共存态与平凡态的行波存在性，并分析了其单调性与渐近稳定性。