Chemostat 中单营养食物链模型的全局稳定性分析

目的研究一类单营养食物链模型的全局稳定性。方法通过解常微分方程讨论模型平衡点的存在性,应用Hurwitz判别法和特征方程法对模型平衡点的稳定性进行分析。结果得到了该模型的3个平衡点的稳定性的充分条件,并且得到了围绕平衡点E_2(x_1~*,x_2~*)至少存在一个极限环的条件。结论单营养食物链的Chemostat系统不仅可以达到生态平衡,而且还存在达到生态平衡的相对弱化的条件。

The global stability analysis for the single nutrition food chain model in Chemostat

Objective— To study the global stability for a class of single nutrition food chain mod-el.Methods—The existence of equilibrium points of the model is discussed by solving ordinary differ-ential equations.The stability of the equilibrium points is analyzed with Hurwitz discriminant method and characteristic equation method.Results—The sufficient conditions for the stability of the three e-quilibrium points of the model are obtained,and the condition that at least one limit cycle centers on the equilibrium point E 2 x *1 ,x *( )2 is obtained.Conclusion—The Chemostat system for the single nutri-tion food chain model can not only reach ecological balance but also have the relative weakening condi-tions of ecological balance.