Sufficient conditions for determining the sign of the wave speed in the Lotka-Volterra competition system

TL;DR

This paper establishes two sufficient conditions to determine the sign of wave speed in bistable Lotka-Volterra competition systems, aiding predictions of species dominance in ecological models.

Contribution

It introduces new criteria for the sign of wave speed in degenerate Lotka-Volterra systems, advancing understanding of species competition dynamics.

Findings

Provided two sufficient conditions for wave speed sign determination.

Enhanced prediction accuracy for species dominance in competition models.

Contributed to the mathematical theory of traveling waves in ecological systems.

Abstract

This paper mainly focuses on the sign of the wave speed in the Lotka-Volterra competition system of bistable type, also known as the strong-strong competition case. The traveling wave solution of the system is crucial for understanding the long-time behavior of solutions to the Cauchy problem. Specifically, the sign of the wave speed is key to predicting which species will prevail in the competition. In this paper, by studying a degenerate Lotka-Volterra competition system, we propose two sufficient conditions for determining the sign of the wave speed.