一类具有时滞和收获的比率依赖捕食模型的分析

Analysis of a Ratio-dependent Predator-prey System with Time Delay and Harvesting

本文研究了一类具有时滞和捕获的比率依赖捕食模型,首先讨论了系统解的正性和有界性,其次给出了模型平衡点的存在性和稳定性分析,证明了时滞可以导致Hopf分支的产生,最后研究了收获的最优控制问题.

In this paper, we have developed a ratio-dependent predator-prey system with time delay and harvesting.Positivity and boundedness of the system are discussed, the existence and stability of all equilibria are investigated. Some criteria for Hopf bifurcation are obtained by analysing the corresponding characteristic equation.Furthermore, an optimal harvest policy is presented by applying the Pontryagin’s maximum principle. Numerical simulations are implemented to support our analytical results.