一类单种群系统正周期解及其稳定性

On Positive Periodic Solutions of a Class of Nonlinear Single Species Systems

考虑周期单种群模型 dxdt=xg( t,x)± p( t,x)的正周解及其稳定性 .证明了在一定条件下 ,系统存在全局吸引的正周期解 .给出了系统存在两个正周期解的充分条件 ,同时也给出了种群灭绝的条件 .这些结果用于 Logistic模型和 Odum模型 ,得到了被开发的周期 Logistic模型存在全局吸引的正周期解 ;被开发了的周期 Odum模型只存在两个正周期解 ,其中之一吸引初值大于一个定数的所有解 。

The single species periodic system d x d t=xg(t,x)±p(t,x) is discussed. Some results on positive periodic solutions and their properties are given. These results are applied to discuss Logistic model and Odum models with harvesting. Some new results are obtained.