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Consider the nonautonomous delay-Logistic equation
\[x'(t)=r(t)x(t)[1-b_1x(t-\tau_1)-b_2x(t-\tau_2)], \quad t\ge 0.\]
We obtain sufficient conditions for the positive steady state $x^* =1/(b_1+b_2)$ to be a global attractor. An application of our result also solves a conjecture of Gopalsamy.
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K. Gopalsa.my, "Global stability in the delay Logistic equations with discrete delays," Houston Journal of Mathematics, 16 (1990), 347-356.
S. M. Lenhart, Travis C. C., "Global stability of a biological model with time delay," Proc. of Amer. Math. Soc.., 96 (1986), 75-78.
K. Gopalsamy, Stability and Oscillation in Delay Differential Equations of Population Dynamies, Kluwer Academic Publishers Boston, 1992, P.60.
K. Gopalse.my, B. S. Lalli, "Oscillation and asymptotic behavior of a. multiplicative delay Logistic equation," Dynamics and Stability of Systems, 1 (1992), 35-42.
A. J. Nicholson, "An outline of the dynamics of animal populatons," Austmlian Journal of Zoology, 2 (1954), 651-663.
G. E. Hutchinson, "Circular causal systems in ecology," Annal. of the New York Academy Sciences, 50 (1948), 221-246.