摘要
文章研究一类食饵具常数投放且增长率含h(x)的食饵-捕食系统。利用常微分方程定性和稳定性理论分析了平衡点的性态,借助Dulac函数法得到了正平衡点全局渐近稳定的充分条件,最后利用Poincare-Bendixson环域定理和张芷芬唯一性定理,证明了极限环存在唯一的充分条件,并给出了数值模拟结果。
In this paper,we study a qualitative analysis of predator-prey system with constant rate stocking and rate function which contains h（x）.By using qualitative theory and stability theory in ordinary differential equation,we analyze the qualitative behavior of equilibrium points.And we find out the sufficient condition of global asymptotic stability of positive equilibrium points.Then,by using Poincare-Bendixson annular region theorem and uniqueness theorem by Zhang Zhi-fen,we prove the sufficient condition of the unique exisitence of limit cycle.At last,we give out the conclusions of the numerical simulation.
出处
《四川理工学院学报（自然科学版）》
CAS
2011年第2期154-158,共5页
Journal of Sichuan University of Science & Engineering(Natural Science Edition)
基金
国家自然科学基金(11072204)
四川省应用基础研究计划(2010JY0079)
成都信息工程学院自然科学发展基金(CSRF200601)
关键词
食饵-捕食系统
平衡点
增长率
极限环
predator-prey system
equilibrium points
growth rate
limit cycle
