非线性泛函微分系统的指数稳定

The exponential stability of a nonlinear functional differential system

利用线性化的方法,解决一类非线性泛函微分系统的周期解的稳定性。如果非线性泛函微分系统的周期的齐次线性微分系统的零解是指数稳定的,那么可以得到非线性泛函微分系统的周期解是指数稳定的。以周期的Lotka-Volterra型n-种群竞争系统为例,得到系统周期解是指数稳定的。

Periodic solutions of a class of nonlinear functional differential system（FDS） am studied using the method of linearization. It shows that the periodic solution of the nonlinear FDS is exponentially stable, if the zero solution of the associated hnear periodic linear homogeneous FDS is exponentially stable. We obtain the exponential stability of a class of periodic Lotka-Volterra type n-species competitive systems.