Positive Periodic Solutions for a Single-Species Model with Delay Weak Kernel and Cycle Mortality

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: $$x'(t) = rx(t)[1 − \frac{1}{K}\int^t_{−∞}αe^ {−α(t−s)} x(s)ds] − a(t)x(t),$$ 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.