一类具有三次方非线性项的Lotka-Volterra型竞争系统的波速符号

The Sign of the Wave Speed for a Class of Lotka-Volterra Competitive Systems with Cubic Reaction Terms

摘要: 本文研究一类带有三次非线性项的Lotka-Volterra竞争扩散模型的双稳行波解的波速符号。该模型用于刻画两类均能释放有毒物质的浮游生物之间的强竞争过程。在一定参数条件下，系统存在连接两个稳定平衡点的行波解。本文重点分析其波速符号的确定条件。通过构造与时间无关的上解，结合比较原理建立了波速为负的若干充分条件。结果表明，在特定参数范围内波速恒为负，这意味着竞争结果中某一物种呈现逆向传播的入侵行为。研究结论为理解种群竞争中的空间传播动态提供了理论依据。

Abstract: This paper investigates the sign of the bistable wave speed for a class of Lotka-Volterra competition-diffusion models with cubic nonlinear terms. This model describes the strong competition between two types of toxin-producing phytoplankton. Under certain parameter conditions, the system has a traveling wave solution connecting two stable equilibrium points. The focus of this paper is on analyzing the sign of the wave speed. By constructing a time-independent upper solution and combining the comparison principle, several sufficient conditions for the wave speed to be negative are established. The results show that the wave speed is always negative within a specific parameter range, indicating that one of the species exhibits an invasive behavior of reverse propagation in the competition outcome. The research conclusion provides a theoretical basis for understanding the spatial propagation dynamics in population competition.