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Persistence and global stability in a delayed Gause-type predator-prey system without dominating instantaneous negative feedbacks. (English) Zbl 1013.34074
For the following predator-prey system without dominating instantaneous negative feedbacks \begin{aligned} \dot{x}_1 &= x_1(t)\left(a_1-a_{11}x_1(t-\tau_1)-a_{12}\frac{x_2(t)}{m+x_1(t)}\right),\\ \dot{x}_2 &= x_2(t)\left(-a_2+a_{21}\frac{x_1(t-\tau_2)}{m+x_1(t-\tau_2)}-a_{22}x_2(t-\tau_3)\right), \end{aligned} the authors obtain sufficient conditions for uniform persistence, and local and global asymptotic stability of a positive equilibrium.

##### MSC:
 34K20 Stability theory of functional-differential equations 92D25 Population dynamics (general)
##### Keywords:
predator-prey system; delay; persistence; stability
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##### References:
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