一类微分方程模型正平衡解的全局稳定性

The Global Stability of the Positive Equilibrium Point to a Model of Differential Equations

研究一类3种群生态系统,分析系统平衡点的稳定性,经历Hopf分支的条件,进一步通过伸缩变换法讨论系统三维正平衡点的局部渐稳定性,得到三维系统正平衡态全局渐近稳定的一个充分条件.

A type of ecological system of three populations is studied.The stability of system equilibrium point and the existence condition of Hopf bifurcation as well as the stability of hence generated periodic solution are analyzed,then established the local stability of 3-D positive equilibrium point by means of the stretching method.The sufficient conditions of the global stability of the nonlinear systems is obtained.