## Almost periodic solution of a modified Leslie-Gower predator-prey model with Beddington-DeAngelis functional response and feedback controls.(English)Zbl 1406.92539

Summary: We consider a modified Leslie-Gower predator-prey model with the Beddington-DeAngelis functional response and feedback controls as follows: $$\dot{x} \left(t\right) = x \left(t\right) \left(a_1 \left(t\right) - b \left(t\right) x \left(t\right) - c \left(t\right) y \left(t\right) / \left(\alpha \left(t\right) + \beta \left(t\right) x \left(t\right) + \gamma \left(t\right) y \left(t\right)\right) - e_1 \left(t\right) u \left(t\right)\right)$$, $$\dot{u} \left(t\right) = - d_1 \left(t\right) u \left(t\right) + p_1 \left(t\right) x \left(t - \tau\right)$$, $$\dot{y} \left(t\right) = y \left(t\right) \left(a_2 \left(t\right) - r \left(t\right) y \left(t\right) / \left(x \left(t\right) + k \left(t\right)\right) - e_2 \left(t\right) \nu \left(t\right)\right)$$, and $$\dot{\nu}(t) = - d_2(t) \nu(t) + p_2(t) y(t - \tau)$$. Sufficient conditions which guarantee the permanence and existence of a unique globally attractive positive almost periodic solution of the system are obtained.

### MSC:

 92D25 Population dynamics (general) 34C25 Periodic solutions to ordinary differential equations
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### References:

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