Permanence for two-species lotka-volterra systems with delays.
The permanence of the following Lotka-Volterra system with time delays x '(1) ( t ) = x(1) ( t ) [ r(1) - a(1)x(1) ( t ) + a(11)x(1) ( t - tau(11) ) + a(12)x(2) ( t - tau(12) ) ] x '(2) ( t ) = x(2) ( t ) [ r(2) - a(2)x(2) ( t ) + a(21)x(1) ( t - tau(21) ) + a(22)x(2) ( t - tau(22) ) ] is considered.With intraspecific competition, it is proved that in competitive case, the system is permanent if and only if the interaction matrix of the system satisfies condition (C1) and in cooperative case it is proved that condition (C2) is sufficient for the permanence of the system.
Lin
Suqing
S
Department of Mathematics, Sichuan Normal University, Chengdu 610068, China. suqinglin05@163.com.
Lu
Zhengyi
Z