基于根轨迹法的海洋生态模型稳定性分析

摘要

A stability analysis is derrived for a nonlinear ocean ecological model. By using the method of generalized root locus the paper gets the conclusion that initial nutrient input influences the system stability, which is further proved by space trajectory. The analysis shows that the system is stable when the growth rate of phytoplankton and the initial nutrient input are both higher than the rate of mortality and the loss of nutrient. The system dynamic prosperities decrease with the increasing of the growth rate of phytoplankton and the initial nutrient input.%本文对一类非线性海洋生态模型进行了稳定性分析,并通过广义根轨迹的分析得出,初始时刻营养盐的不同输人对系统稳定性的影响,并用相轨迹图加以验证.通过稳定性分析可知,当浮游植物的生长率和初始时刻营养盐的输入均大于浮游植物的死亡率和营养盐的流失时,系统存在稳定状态.若浮游植物的生长率和初始时刻营养盐的输人增大时,系统的动态性能减少,即系统会更快的趋于稳定状态.