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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

${x}_{1}^{{}^{\text{'}}}\left(t\right)=-{\alpha }_{1}\left(t\right){x}_{1}\left(t\right)+{\beta }_{1}\left(t\right){x}_{2}\left(t\right)+\sum _{j=1}^{m}{c}_{1j}\left(t\right){x}_{1}\left(t-{\tau }_{1j}\left(t\right)\right){e}^{-{\gamma }_{1j}\left(t\right){x}_{1}\left(t-{\tau }_{1j}\left(t\right)\right)},$
${x}_{2}^{{}^{\text{'}}}\left(t\right)=-{\alpha }_{2}\left(t\right){x}_{2}\left(t\right)+{\beta }_{2}\left(t\right){x}_{1}\left(t\right)+\sum _{j=1}^{m}{c}_{2j}\left(t\right){x}_{1}\left(t-{\tau }_{1j}\left(t\right)\right){e}^{-{\gamma }_{1j}\left(t\right){x}_{1}\left(t-{\tau }_{1j}\left(t\right)\right)}·$

##### MSC:
 34K60 Qualitative investigation and simulation of models 34K14 Almost and pseudo-periodic solutions of functional differential equations 34K20 Stability theory of functional-differential equations 92D25 Population dynamics (general)
##### References:
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