非自治时滞捕食–食饵模型正周期解的存在性

The Existence of Positive Periodic Solutions for the Non-Autonomous Time-Delayed Predator-Prey Model

摘要: 本文建立了一个捕食者具有阶段结构的Beddington-DeAngelis型功能反应的时变捕食–食饵模型，通过定义两个正常数R*和R_*得到了系统解持久或灭绝的充分条件。若R_*>1，则系统的解是一致持久的，若R*<1，则捕食者种群灭绝。此外根据度理论的连续性定理，当系统解一致持久时，得到了系统至少存在一个正周期解。数值模拟验证并补充了定性理论分析的结果，得出幼年捕食者较短的成熟期有利于食饵和捕食者种群的持久生存。

Abstract: In this paper, a time-varying predator-prey model of Beddington-DeAngelis functional response with stage-structured is established. By defining two normal numbers R* and R_*, we obtain suf-ficient conditions for the persistence or extinction of system solutions. If R_*>1, the solution of the system is uniformly persistent; if R*<1, the predator will be extinct. In addition, according to the continuous theorem of degree theory, when the system solution is uniformly persistent, it is concluded that the system has at least one positive periodic solution. Numerical simulation verifies and complements the results of qualitative theoretical analysis, and concludes that the short maturity period of immature predators is beneficial to the persistent survival of prey and predator populations.