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Periodic solutions of a discrete two-species competitive model with stage structure. (English) Zbl 1145.34334
Summary: We investigate the following discrete periodic stage-structure model. ${x}_{1}\left(k+1\right)={x}_{1}\left(k\right)exp\left(-{a}_{1}\left(k\right)+{b}_{1}\left(k\right)\frac{{x}_{2}\left(k\right)}{{x}_{1}\left(k\right)}\right)$, ${x}_{2}\left(k+1\right)={x}_{2}\left(k\right)exp\left({a}_{2}\left(k\right)\frac{{x}_{1}\left(k\right)}{{x}_{2}\left(k\right)}-{b}_{2}\left(k\right)-c\left(k\right){x}_{2}\left(k\right)-{\beta }_{1}\left(k\right){x}_{3}\left(k\right)\right)$, ${x}_{3}\left(k+1\right)={x}_{3}\left(k\right)exp\left(d\left(k\right)-exp\left(k\right){x}_{3}\left(k\right)-{\beta }_{2}\left(k\right){x}_{2}\left(k\right)\right)$. The sufficient and realistic conditions are obtained for the existence of a positive periodic solution of this system.
##### MSC:
 34C25 Periodic solutions of ODE 92D25 Population dynamics (general)
##### References:
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