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

Chuangxia Huang; Hua Zhang; Lihong Huang

doi:10.3934/cpaa.2019150

Article Contents

2019, Volume 18, Issue 6: 3337-3349. Doi: 10.3934/cpaa.2019150

This issue Previous Article The regularity of a degenerate Goursat problem for the 2-D isothermal Euler equations Next Article A note on multiplicity of solutions near resonance of semilinear elliptic equations

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
^* Corresponding author

Received: September 30, 2018

Revised: January 31, 2019

Published: May 2019

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)

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Abstract

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.

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Mathematics Subject Classification: 34C25; 34K13.

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Figure 1. Numerical solutions $ x(t) $ to example (4.1) with initial values: $ 2, 4, 6 $

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