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Existence of positive periodic solutions for a class of nonautonomous difference equations. (English) Zbl 1093.39014
The subject of the paper is the existence of positive periodic solutions for the nonautonomous difference equations $$\Delta x(k)=a(k)x(k)-f(k,u(k))$$ and $$\Delta x(k)=-a(k)x(k)+f(k,u(k)),$$ where $\Delta x(k)=x(k+1)-x(k)$, and for $k,s\in \mathbb{Z}$, $$u(k)=\Big(x(g_1(k)),x(g_2(k)),\dots,x(g_{n-1}(k)), \sum_{s=-\infty}^{k}h(k-s)x(s)\Big)\,.$$ These two equations include many mathematical ecological difference models. Using the Krasnoselskii fixed point theorem in cones, the author establishes some sufficient criteria, which are easily verifiable and generalize related studies in the literature. At last, the author illustrates his main results by numerical simulations.

39A11Stability of difference equations (MSC2000)
92B05General biology and biomathematics
92D25Population dynamics (general)
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