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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.