n-物种Lotka-Volterra模型在周期脉冲下的持久性
Persistence of n-Species Lotka-Volterra Models with Periodic Pulses
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中文总结 AI 辅助
针对周期脉冲干扰下的n-物种Lotka-Volterra模型，提出基于Morse分解和加权长期增长率的持久性充分条件，并证明其鲁棒性，应用于癌症化疗与农业害虫防治案例。
中文摘要 AI 辅助
周期性脉冲干预在生物种群管理中自然出现，包括化疗、农药施用和传染病治疗。我们针对受周期性乘性脉冲扰动影响的n-物种种群模型，发展了持久性的一般条件。我们的主要结果在灭绝集的Morse分解上，以加权长期增长率的形式给出了持久性的充分条件，明确区分了连续种群动力学与周期脉冲各自的贡献。为建立该结果，我们将脉冲系统转化为一个相关的自治连续时间动力系统，并利用这一对应关系将经典持久性理论推广到周期脉冲模型。我们进一步证明，在连续动力学、脉冲周期和脉冲效应的足够小扰动下，相同条件蕴含鲁棒持久性。我们以两个受生物防治启发的Lotka-Volterra模型说明该框架：化疗敏感与化疗耐药癌细胞之间的竞争，以及使用农药和寄生蜂对农业害虫的综合防治。这些例子展示了干预频率和强度如何与潜在生态相互作用共同决定种群是共存还是被排除。我们的结果为分析遭受重复离散扰动的生态系统的持久性提供了一个一般框架。
英文摘要
Periodic impulsive interventions arise naturally in the management of biological populations, including chemotherapy, pesticide application, and infectious-disease treatment. We develop general conditions for permanence in n-species population models subject to periodic multiplicative pulse disturbances. Our main result provides a sufficient condition for permanence in terms of weighted long-term growth rates on a Morse decomposition of the extinction set, explicitly separating the contributions of continuous population dynamics from those of the periodic pulse. To establish this result, we transform the impulsive system into an associated autonomous continuous-time dynamical system and use this correspondence to extend classical permanence theory to periodically pulsed models. We further show that the same conditions imply robust permanence under sufficiently small perturbations to the continuous dynamics, pulse period, and pulse effects. We illustrate the framework with two Lotka-Volterra models motivated by biological control: competition between chemotherapy-sensitive and chemotherapy-resistant cancer cells, and integrated control of an agricultural pest using pesticides and parasitoids. These examples demonstrate how intervention frequency and intensity interact with underlying ecological interactions to determine whether populations coexist or are excluded. Our results provide a general framework for analyzing persistence in ecological systems subject to repeated discrete disturbances.
发表机构
- Oregon State University（俄勒冈州立大学）
- Arcadis（阿科玛）
机构由 AI 辅助整理，请以论文原文为准。
