一类具有稀疏效应的捕食与被捕食系统

A Class of Predator-prey System with Sparse Effect

针对一类稀疏效应下具有HollingⅣ功能反应的捕食-被捕食系统,应用常微分方程定性理论,分析了系统平衡点的存在性,研究了平衡点的局部稳定性及全局稳定性,讨论了系统解的正向有界性,最后利用环域定理分析了极限环存在的条件.

For a class of Holling Ⅳ functional response predator-prey system with sparse effect,we analyze the existence of the equilibrium,study the local stability and global stability of equilibriums,and discuss the positive boundedness of the solutions by using qualitative theorem of ordinary differential equations. Finally,the existence of limit cycle is analyzed by using Bendixson theorem.