一类具有常数避难所与收获率的捕食-食饵模型的稳定性分析

Analysis of a Harvested Predator-Prey Model Incorporating a Constant Prey Refuge

研究了一类具有常数避难所与线性收获率的捕食-食饵模型的动力形态。应用Gronwall不等式得到了系统解的一致有界性。利用平面系统的定性与稳定性理论以及规范型理论,分析了系统的局部性态和全局稳定性,得到了平衡点的分类。这些平衡点可以是鞍点、稳定结点、稳定焦点以及鞍结点等。最后进行了数值模拟,验证了理论结果。

In this paper,the dynamical behaviors of a predator-prey model with constant refuge and linear harvesting rates are studied.The local and global properties of the system are discussed.By Gronwall inequality theorem,the uniform boundedness of solutions of the system is obtained.Using the qualitative analysis for the planar system and the normal form theory,the stabilities of the system are analyzed.It shows that the equilibriums can be saddle point,stable node,stable focus or saddle-node.Some numerical simulations are carried out to verify our theoretical results.