一类具有收获率和比率的时滞阶段结构的扩散捕食系统的多重正周期解

Multiple Periodic Solution for a Delayed Stage-structure Predator-prey Systems with Ratio-dependence and Harvesting Rate and Diffusion

近年来,对具有阶段结构的捕食系统周期解存在性问题已有广泛的研究。然而,对具有收获率和比率的时滞阶段结构的扩散捕食系统周期解存在性问题,还未见相关文献发表。因此,本文利用重合度理论中的延拓定理,通过一些分析技巧,获得了一类具有收获率和比率的时滞阶段结构的扩散捕食系统至少存在四个正周期解的一组易于验证的充分条件。

In recent years, the problem of the existence of periodic solutions for stage-structure predator-prey system has been extensively studied. However, so far as the author knows, nobody studies the existence of periodic solutions for a delayed stage-structure predator-prey system with ratio-dependence and harvesting rate and diffusion. In this paper, by developing some technique of analysis and using continuation theorem based on coincidence degree, a set of easily verifiable sufficient conditions are derived for a delayed stage-structure predator-prey system with ratio-dependence and harvesting rate and diffusion, which has at least four positive periodic solutions.