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

2024/08/20 by Dongyuan Xiao, Xiao, Dongyuan · 1 citation
Mathematics · Medicine · #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Biology Tumor Growth #Mathematical and Theoretical Epidemiology and Ecology Models

paper · pdf · doi:10.48550/arxiv.2408.10481

openalex publication_date 2024/08/20 · openalex created_date 2024/10/01 · openalex updated_date 2026/07/28

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.

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• Propagation speed of traveling waves for diffusive Lotka-Volterra system with strong competition

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