一类被开发的Kolmogorov系统的定性分析

Qualitative Analysis of a Kind of Kolmogorov System Exploited

讨论一类食饵种群被开发的捕食系统平衡点的行为和系统的稳定性 .应用向量场分析和解有界但闭轨不存性 ,讨论了平衡点全局稳定的条件 ;应用 Dulac函数法得到闭轨不存在的充分条件 ;应用 Poincare- Bendixson环域定理及张芷芬惟一性定理证明了极限环的存在惟一性 .

The behavior of equilibria and stability of a kind of predator prey system in which the prey is exploited is discussed Constructing by Dulac function,a sufficient condition of the closed orbit is obtained The condition of global stability of equilibria is discussed by the analysis of vector field and the boundness of solution and nonexistence of close orbit The existence and uniqueness of limit cycle is obtained in terms of Poincare Bendixson theorem and Zhang Zhifen uniqueness theorem