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Existence and exponential stability of positive almost periodic solution for Nicholson-type delay systems. (English) Zbl 1232.34111

The authors study existence and exponential stability of positive almost periodic solutions for the following system \[ x^{'}_1(t)=-\alpha_1(t)x_1(t)+\beta_1(t)x_2(t)+ \sum_{j=1}^m c_{1j}(t)x_1(t-\tau_{1j}(t))e^{-\gamma_{1j}(t)x_1(t-\tau_{1j}(t))}, \]
\[ x^{'}_2(t)=-\alpha_2(t)x_2(t)+\beta_2(t)x_1(t)+ \sum_{j=1}^m c_{2j}(t)x_1(t-\tau_{1j}(t))e^{-\gamma_{1j}(t)x_1(t-\tau_{1j}(t))}. \]

MSC:

34K60 Qualitative investigation and simulation of models involving functional-differential equations
34K14 Almost and pseudo-almost periodic solutions to functional-differential equations
34K20 Stability theory of functional-differential equations
92D25 Population dynamics (general)
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