Spreading dynamics for the Lotka-Volterra system with general initial supports: the strong competition

TL;DR

This paper analyzes the spreading behavior of a high-dimensional Lotka-Volterra competition model with arbitrary initial supports, providing detailed descriptions of spreading speeds and regions for both species.

Contribution

It introduces geometric concepts to characterize the directional spreading dynamics of two competing species with complex initial distributions.

Findings

Derived precise spreading speeds for both species.

Characterized spreading regions based on initial support geometry.

Extended single-species geometric notions to multi-species competition.

Abstract

This paper studies the spreading dynamics of a high-dimensional strong competition Lotka-Volterra system where two species initially occupy disjoint measurable (possibly unbounded) subsets in $\mathbb{R}^N$, which are called initial support. Recently, Hamel and Rossi [14] introduced some new geometric notions, such as bounded or unbounded directions and positive-distance interior, for single-species equations with general initial supports. Under these notions and appropriate assumptions, we characterize directional spreading behavior for the two-species system: precise spreading speeds and sets for both species are derived.