Abstract
This paper presents the necessary and sufficient condition for the global stability of the following Lotka–Volterra cooperative or competition system with time delays: x′(t) = x(t)[r 1 − ax(t) + αx(t − τ 11) + βy(t − τ 12)], y′(t) = y(t)[r 2 − ay(t) + βx(t − τ 21) + αy(t − τ 22)]. It is showed that the positive equilibrium of the system is globally asymptotically stable for all delays τ ij ≥ 0 ( i, j = 1, 2) if and only if |β| < a − α and |β| ≤ a + α hold.
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