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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
\[ \dot x_1(t)=x_1(t)[r_1(t)-a_{11}(t)x_1(t-\tau(t))-a_{12}(t)x_2(t)/(m^2+x_1^2(t))], \]
\[ \dot x_2(t)=x_2(t)[r_2(t)-a_{21}(t)x_2(t)/x_1(t)], \]
are obtained, where \(x_1(t)\) and \(x_2(t)\) stand for the density of the prey and the predator, respectively, and \(m\neq 0\) is a constant. \(\tau(t)\geq 0\) stands for the time delays due to negative feedback of the prey population.

MSC:

34K25 Asymptotic theory of functional-differential equations
92D25 Population dynamics (general)
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References:

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