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| Positive Periodic Solutions for a Single-species Model with Delay Weak Kernel and Cycle Mortality |
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| KeyWord:Positive periodic solutions Single-species model Delay Cycle mortality |
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| Abstract: |
| In this paper, by using the Krasnoselskii's fixed-point theorem, we study the existence of positive periodic solutions of the following single-species model with delay weak kernel and cycle mortality:
\begin{align*}
x'(t) = rx(t) \Big[1-\frac{1}{K}\int_{-\infty}^{t}\alpha e^{-\alpha(t-s)}x(s)ds\Big] -a(t)x(t),
\end{align*}
and get the necessary conditions for the existence of positive periodic solutions. Finally, an example and numerical simulation are used to illustrate the validity of our results. |
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