Permanence for two-species Lotka-Volterra systems with delays

The permanence of the following Lotka-Volterra system with time delays <(x) over dot>(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) over dot>(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 incompetitive case, the system is permanent if and only if the interaction matrix of the system satisfies condition (C1) and incooperative case it is proved that condition (C2) is sufficient for the permanence of the system.