N+M维Lotka—Volterra捕食—竞争时滞系统的渐近性

Asmptotic behavior of N+M dimensions Lotka-Volterra predator-competition delay system

研究了N+M维Lotka—Volterra捕食—竞争时滞系统的持久性和全局渐近稳定性,分别利用比较原理和构造Lyapunov函数方法得到了系统持久生存与全局渐近稳定性的充分条件,举例说明定理的可行性,且利用matlab绘出图像加以验证.

N＋M dimension nonautonomous lotka-volterra predator-competition delay system was investigated,sufficient conditions were derived for uniform persistence of this by using the comparison;when the system was a periodic system,sufficient conditions were obtained that guarantee the existence,uniqueness and global attractivity of the positive periodic solution by applying the Brouwer fixed theorem and the method of constructing Lyapunov function,theorems were realized by giving an example and picture was drawn by using software of matlab.