一类具时滞的Lotka-Volterra系统的持久性和稳定性

一类具时滞的Lotka Volterra系统的持久性和稳定性(涪陵师范学院数学系,重庆涪陵408003)1　引言生态系统的持久性与全局渐进稳定性是受到学术界重视的问题1～4].本文研究如下一类Lotka Volterra时滞系统: x1(t)=x1(t)b1(t)-a1(t)x1(t)-d2(t)x2(t)-d3(t)x3(t)], x2(t)=x2(t)-b2(t)+k2(t)∫0-τ1μ1(θ)x1(t+θ)dθ-a2(t)x2(t)-a3(t)x3(t)],(1) x3(t)=x3(t)-b3(t)+k3(t)∫0-τ2μ2(θ)x1(t+θ)dθ-e2(t)x2(t)-a3(t)x3(t)].这里bi(t),ai(t),(i=1,2,3),di(t),ei(t),ki(t)(i=2,3)是连续函数,且有正的下界和上界.μi(s)(i=1,2)是-τi,0]上…

On the Permanence and Stability for a Class of Lotka-Volterra System with Time Delay

By the Liapunov function and differential inequality, the author studied a class of Lotka-Volterra system with time delay. It is proved that the system can be permanent under some conditions and its any positive solution in globally asymptotically stable under the approiate conditions.