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Permanence of a semi-ratio-dependent predator-prey system with nonmonotonic functional response and time delay. (English) Zbl 1182.34100

Summary: Sufficient conditions for permanence of the semi-ratio-dependent predator-prey system with nonmonotonic functional response and time delay

x ˙ 1 (t)=x 1 (t)[r 1 (t)-a 11 (t)x 1 (t-τ(t))-a 12 (t)x 2 (t)/(m 2 +x 1 2 (t))],
x ˙ 2 (t)=x 2 (t)[r 2 (t)-a 21 (t)x 2 (t)/x 1 (t)],

are obtained, where x 1 (t) and x 2 (t) stand for the density of the prey and the predator, respectively, and m0 is a constant. τ(t)0 stands for the time delays due to negative feedback of the prey population.

34K25Asymptotic theory of functional-differential equations
92D25Population dynamics (general)