AI 中文总结
研究高维植物-消费者反应扩散系统中行波，基于新混合下解构造证明特定条件下速度集合关系，通过多种论证得出行波存在性及速度上下界，还通过双物种系统构造明确波表明sC^ex非最大波速。
AI 中文摘要
我们研究一类具有N个竞争植物物种和N个相关消费者种群的高维植物-消费者反应扩散系统中的行波。消费者方程在灭绝状态下是线性退化的。在弱相互作用条件‖K‖∞<1下，系统存在唯一的正共存平衡。定义了一些参数，设S是允许存在从灭绝到共存的严格正行波的速度集合。若sP<sC^ex，我们证明(sP,sC^ex)⊆S⊆[sP,sC^nec)。存在性结果基于一种新的混合下解构造。低于sP不存在行波由一个斯特姆型振荡论证得出，前沿渐近性和一个里卡蒂交叉论证得出通用上界s<sC^nec。最后，对于一个固定的双物种系统，构造了一个明确的波，表明sC^ex只是一个构造阈值，而非内在最大波速。
英文摘要
We study traveling waves in high-dimensional plant--consumer reaction--diffusion systems with $N$ competing plants and $N$ associated consumers. We focus on the degenerate case in which consumer growth vanishes when plant populations are zero, so the standard Fisher--KPP linearization does not determine the leading-edge behavior. Under a weak-interaction condition, we identify a plant-driven lower threshold $s_{\mathrm P}$, a constructive upper threshold $s_{\mathrm C}^{\mathrm{ex}}$, and a universal necessary upper threshold $s_{\mathrm C}^{\mathrm{nec}}$, and prove $(s_{\mathrm P},s_{\mathrm C}^{\mathrm{ex}})\subseteq \mathcal S\subseteq[s_{\mathrm P},s_{\mathrm C}^{\mathrm{nec}})$, where $\mathcal S$ is the set of speeds admitting positive extinction-to-coexistence waves. Existence follows from new lower solutions that remove previously imposed diffusion and compatibility restrictions. Nonexistence below $s_{\mathrm P}$ follows from a Sturm argument, while center-manifold analysis and a Riccati crossing argument yield the finite upper-speed obstruction. An explicit two-species wave beyond $s_{\mathrm C}^{\mathrm{ex}}$ shows that this constructive threshold is not the true maximal speed.
Comments32 pages; fixed minor typos
