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

作　　者：谢明铭 

机构地区：[1]广州大学数学与信息科学学院,广东 广州

出　　处：《应用数学进展》2024年第4期1810-1816,共7页Advances in Applied Mathematics

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。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.

关 键 词：单种群模型 ALLEE效应 稳定性 时滞 

分 类 号：O17[理学—数学]