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Zbl 1232.34111
Wang, Wentao; Wang, Lijuan; Chen, Wei
Existence and exponential stability of positive almost periodic solution for Nicholson-type delay systems. (English)
[J] Nonlinear Anal., Real World Appl. 12, No. 4, 1938-1949 (2011). ISSN 1468-1218

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

MSC 2000:: *34K60 Applications of functional-differential equations
34K14 Almost periodic solutions of functional differential equations
34K20 Stability theory of functional-differential equations
92D25 Population dynamics

Keywords: Nicholson-type delay system; existence of almost periodic solutions; exponential stability

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