一类微分方程系统正平衡解的存在性与全局稳定性

Existence and Global Stability of Positive Equilibrium Point to a System of Differential Equations

中文关键词:  食物链模型  正平衡点  伸缩变换  Liapunov函数  全局渐近稳定.

英文关键词:food chain model  positive steady-state  stretching  Liapunov function  global asymptotical stability.

中文摘要:

      本文研究了一个自治的非线性微分方程系统, 得到了系统正平衡点存在唯一的充分条件,通过伸缩变换法讨论了正平衡点局部稳定性, 并运用构造Liapunov函数方法得到了它的全局渐近稳定性.

英文摘要:

      This paper deals with an autonomous nonlinear system of differential equations. We obtain the existence-uniqueness of positive equilibrium point to the problem, and then establish the local stability and the global asymptotic stability of the positive equilibrium point by means of the stretching method and the Liapunove function method, respectively.