摘要
在食饵种群具有常数收获率的生态系统的基础上,研究了一类捕食者种群、食饵种群同时具有收获率的微分生态系统,其中食饵种群、捕食者种群都具有密度制约。应用微分方程定性理论讨论了系统的平衡点,对平衡点的渐近稳定性做出了分析,得出:当给定参数满足一定条件时系统不存在极限环。利用Bendixson环域定理证明了该系统极限环的存在性。
Based on ecosystem with constant harvesting rate for preys,a differential ecosystem with harvesting rates for preys and predators is studied.The system＇s equilibrium point is discussed by using differential equations qualities theory and the stability of equilibrium point is analysed.The nonexistence of the system＇s limit cycle is obtained if the given parameter satisfied certain conditions.By using Bendixson theorem,the existence of the system＇s limit cycle are proved.It is obtained that the density of preys and predators are stable under some conditions.
出处
《广东石油化工学院学报》
2011年第3期70-72,82,共4页
Journal of Guangdong University of Petrochemical Technology
基金
国家自然科学基金资助项目(11072090)
蚌埠学院自然科学基金资助项目(2010ZR16)
关键词
微分生态系统
收获率
稳定性
极限环
differential ecosystem
harvesting rates
stability
limit cycle
