总资源相等的周期竞争扩散系统中扩散对比诱导的动力学
Diffusion contrast induced dynamics in a time-periodic competition-diffusion system with equal total resources
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中文总结 AI 辅助
本文针对总资源相等的周期竞争扩散系统，结合渐近分析与主特征值理论，揭示时间周期与空间异质性的相互作用可颠覆经典的“慢扩散者总是占优”原理，获得了丰富的生态动力学结果。
中文摘要 AI 辅助
本文研究了一个时空异质的周期竞争扩散系统，其中两个物种具有不同的固有增长率，但每个周期的总资源相等。利用渐近分析和主特征值理论，我们系统地考察了其动力学：当两个扩散率均较小时，时间平均资源差异的空间异质性会导致一致持续、稳定共存和渐近空间分离；而时间平均资源差异的空间均匀性则会产生多种状态——快扩散者选择、参数依赖共存或慢扩散者占优，这些状态由不同结构条件下的平滑阈值曲线分隔。在至少一个扩散率较大的状态下，我们对局部动力学进行了详细分类，明确划分了稳定共存、竞争排斥和新型双稳态情景的参数区域，其中两个半平凡周期解均线性稳定，同时还存在一个不稳定共存状态。我们进一步刻画了混合尺度扩散极限下正解的渐近轮廓。研究结果表明，时间周期性与空间异质性的相互作用可颠覆经典的“慢扩散者总是占优”原理，产生丰富得多的生态结果。
英文摘要
This paper investigates a time-periodic, spatiotemporally heterogeneous competition-diffusion system, where two species have different intrinsic growth rates but equal total resources per period. Using asymptotic analysis and principal eigenvalue theory, we systematically examine its dynamics. When both diffusion rates are small, spatial heterogeneity of the difference in time-averaged resources leads to uniform persistence, stable coexistence, and asymptotic spatial segregation; whereas its spatial uniformity produces multiple regimes--fast-diffuser selection, parameter-dependent coexistence, or slow-diffuser dominance--separated by smooth threshold curves under different structural conditions. In the regime where at least one diffusion rate is large, we obtain a detailed classification of the local dynamics, with sharp delineation of parameter regions for stable coexistence, competitive exclusion, and a novel bistable scenario, where both semi-trivial periodic solutions are linearly stable while an unstable coexistence state also exists. We further characterize the asymptotic profiles of positive solutions in the mixed-scale diffusion limit. Our results show that the interplay between temporal periodicity and spatial heterogeneity can overturn the classical "slower diffuser always prevails" principle, leading to a substantially richer range of ecological outcomes.
