具有季节演替的三竞争物种 Lotka-Volterra 模型的永久持续与非永久持续分类
Classification of permanence and impermanence for a Lotka-Volterra model of three competing species with seasonal succession
AI总结：
针对具有季节演替的三竞争物种 Lotka-Volterra 模型，论文利用承载单形按参数不等式完整划分永久持续与非永久持续，并数值揭示永久持续情形中存在不变闭曲线。
摘要：
本文关注具有季节演替的三竞争物种 Lotka-Volterra 模型的永久持续性。基于承载单形（即一个余维为一的全局吸引超曲面）的存在性，我们依据该模型参数上的不等式，对永久持续与非永久持续给出了完整分类。此外，我们通过数值计算表明，在永久持续类别中可能出现不变闭曲线，这意味着永久持续类别中相关 Poincare 映射的正不动点并不总是全局渐近稳定的。
英文摘要：
In this paper, we are concerned with the permanence of a Lotka-Volterra model of three competing species with seasonal succession. Based on the existence of a carrying simplex, that is a globally attracting hypersurface of codimension one, we provide a complete classification of the permanence and impermanence in terms of inequalities on the parameters of this model. Moreover, we numerically show that invariant closed curves can occur in the permanent classes, which means that the positive fixed point of the associated Poincare map in the permanent classes is not always globally asymptotically stable.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
