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Stability and delays in a predator-prey system. II. (English) Zbl 0952.34061
[For part Iss see J. Math. Anal. Appl. 198, No. 2, 355-370, Art. No. 0087 (1996; Zbl 0873.34062).]
Under some assumption on system’s coefficients and delay functions it is shown that the classical Lotka-Volterra system \[ \begin{aligned} {dx\over dt} &= x(t)[r_1- a_{11}x(t- \sigma_{11}(t))- a_{12}y(t- \sigma_{12}(t))],\\ {dy\over dt} &= y(t)[-r_2+ a_{21}x(t- \sigma_{21}(t))- a_{22}y(t- \sigma_{22}(t))],\end{aligned} \] with \(r_i>0\), \(a_{ij}> 0\), has a unique positive equilibrium that is globally attractive with respect to the set of positive solutions.

MSC:
34K20 Stability theory of functional-differential equations
92D25 Population dynamics (general)
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