两物种Lotka–Volterra竞争-扩散系统中双稳行波前的传播方向
Propagation Direction of Bistable Traveling Fronts in the Lotka--Volterra Competition--Diffusion System
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中文总结 AI 辅助
针对两物种Lotka–Volterra竞争-扩散系统强竞争下双稳行波前传播方向问题，结合麦克斯韦型恒等式与相平面刚性论证建立波速为零的全局充要判据，明确了该系统强竞争参数区域内的传播方向。
中文摘要 AI 辅助
我们研究强竞争条件下两物种Lotka–Volterra竞争-扩散系统中双稳行波前的传播方向，波速符号的完整刻画长期以来是未解决的问题。我们结合麦克斯韦型恒等式与相平面刚性论证，建立首个波速为零的全局充要判据，该判据给出唯一零速度阈值，确定对称情形下的阈值值及两个极端 regime 中的极限值，由此明确强竞争参数区域内的传播方向。
英文摘要
We study the propagation direction of bistable traveling fronts in the two-species Lotka--Volterra competition--diffusion system under strong competition. A complete characterization of the sign of the wave speed has remained a long-standing unsolved problem. We establish the first global necessary and sufficient criterion for zero wave speed by combining a Maxwell-type identity with a phase-plane rigidity argument. This criterion yields a unique zero-speed threshold, identifies its value in the symmetric case and its limiting values in two extreme regimes, and consequently determines the propagation direction throughout the strong-competition parameter region.
