一类非线性微分动力系统的定性分析

Qualitative Analysis of a Nonlinear Differential Dynamic System

本文研究了一类非线性微分动力系统０，ｂ＞０，Ｐ＞０）的定性行为，完整地解决了系统的极限环的不存在性、存在性和唯一性问题。得到系统有唯一极限环当且仅当（Ｐ一１）ａ－ｂ＞（ａ＋ｂ）^（Ｐ＋１）

The qualitative behavior of the solution of a non-linear differential dynamical system (a > 0, b > 0, P > 0) is discussed. The conditions of nonexistence, existence and uniqueness of limit cycles of the system are obtained, and it is proved that the system admits a unique limit cycle if and only if (P - 1)a - 6 > (a + b)~p+1.