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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
Author NameAffiliation
Ceyu Lei Department of Mathematics, Northwest Normal University, Lanzhou, Gansu 730070, China 
Xiaoling Han Department of Mathematics, Northwest Normal University, Lanzhou, Gansu 730070, China 
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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.