受捕食影响的单种群时滞模型的动力学
Dynamics of a Delayed Single Population Model with a Predation
DOI: 10.12677/aam.2024.134170, PDF,   
作者: 谢明铭：广州大学数学与信息科学学院，广东 广州
关键词: 单种群模型；Allee效应；稳定性；时滞；Single-Population Model； Allee Effect； Stability； Delay
摘要: 本文研究了一类受捕食影响的单种群时滞模型，其中捕食因素导致模型出现强/弱Allee效应。我们重点分析了时滞对稳定性的影响，并通过数值模拟验证我们的理论结果。结果表明小时滞有助于种群维持稳定生存状态，而随着时滞的增大，种群可能呈现周期振荡；而当时滞充分大于临界值时，种群最终会灭绝。此外我们研究发现，可以通过调控时滞确保种群的持续生存。
Abstract: This paper considers a single-species model with delay, influenced by predation, where predation may induce strong/weak Allee effects in the model. We focus on analyzing the impact of delay on stability and validate our theoretical findings through numerical simulations. The results indicate that a small delay contributes to the stable survival of the population, while an increase in delay may lead to periodic oscillations. However, when the delay significantly exceeds a critical value, the population ultimately faces extinction. Furthermore, our research finds that regulating the delay can ensure the population’s sustained survival.
文章引用：谢明铭. 受捕食影响的单种群时滞模型的动力学[J]. 应用数学进展, 2024, 13(4): 1810-1816. https://doi.org/10.12677/aam.2024.134170

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