一类时滞单种群模型的稳定性

The Stability of a Single Species Model with Time Delay

研究了一类具有强时滞的Logistic单种群模型。首先,得出系统存在一致持久性条件和全局吸引的条件;其次,给出具体的核函数,通过链变换把模型转化为定常的二维系统和三维系统,利用线性近似方程和Routh-Hurwitz准则分析该系统平衡点的稳定性。

In this paper, Logistic single population model with strong time delay is investigated. First, the condition of system uniform persistence and global appeal; Second, gives a specific kernel function, through the chain of transform the model into time-invariant system of two-dimensional and three-dimensional system, using the linear approximation equation and Routh Hurwitz criterion analyze the stability of the system balance.