关于离散种群模型稳定性的一则注释。

A note on stability of discrete population models.

作者信息

Huang Y

出版信息

Math Biosci. 1989 Aug;95(2):189-98. doi: 10.1016/0025-5564(89)90032-1.

PMID:2520185

Abstract

P. Cull (1981) and G. Rosencranz (1983) studied a discrete population model described by the first-order difference equation xt+1 = g(xt) and obtained an important result on the global stability of the equilibrium point means when g(x) has only one extreme point (a maximum) in (0, means). Motivated by work of M. Kot and W. M. Schaffer (1984), a more general case is considered in which g(x) can have more then one maximum point in (0, means), and results on global stability are obtained. These results are applied to develop tests for global stability of the equilibrium point that imply other results in the literature on global stability.

摘要

P. 卡尔（1981年）和G. 罗森克兰茨（1983年）研究了由一阶差分方程(x_{t + 1} = g(x_t))描述的离散种群模型，并在平衡点均值的全局稳定性方面取得了重要成果，条件是(g(x))在((0,均值))内仅有一个极值点（最大值）。受M. 科特和W. M. 谢弗（1984年）工作的启发，本文考虑了一种更一般的情况，即(g(x))在((0,均值))内可以有多个最大值点，并得出了全局稳定性的结果。这些结果被用于开发平衡点全局稳定性的检验方法，这些方法蕴含了文献中关于全局稳定性的其他结果。