# American Institute of Mathematical Sciences

November  2019, 18(6): 3337-3349. doi: 10.3934/cpaa.2019150

## Almost periodicity analysis for a delayed Nicholson's blowflies model with nonlinear density-dependent mortality term

 1 School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha 410114, Hunan, China 2 Hunan Provincial Key Laboratory of Mathematical Modeling, and Analysis in Engineering, Changsha 410114, Hunan, China

* Corresponding author

Received  October 2018 Revised  February 2019 Published  May 2019

Fund Project: The work is partially supported by the National Natural Science Foundation of China (Nos.71471020, 11771059, 51839002); Hunan Provincial Natural Science Foundation of China (No. 2016JJ1001); Scientific Research Fund of Hunan Provincial Education Department (Nos. 15A003, 16C0036).

This paper mainly investigates a class of almost periodic Nicholson's blowflies model involving a nonlinear density-dependent mortality term and time-varying delays. Combining Lyapunov function method and differential inequality approach, some novel assertions are established to guarantee the existence and exponential stability of positive almost periodic solutions for the addressed model, which generalize and refine the corresponding results in some recent published literatures. Particularly, an example and its numerical simulations are given to support the proposed approach.

Citation: Chuangxia Huang, Hua Zhang, Lihong Huang. Almost periodicity analysis for a delayed Nicholson's blowflies model with nonlinear density-dependent mortality term. Communications on Pure & Applied Analysis, 2019, 18 (6) : 3337-3349. doi: 10.3934/cpaa.2019150
##### References:

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##### References:
Numerical solutions $x(t)$ to example (4.1) with initial values: $2, 4, 6$
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