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Stability of Almost Periodic Nicholson’s Blowflies Model Involving Patch Structure and Mortality Terms

Part of: Qualitative theory Functional-differential and differential-difference equations

Published online by Cambridge University Press:  23 December 2019

Chuangxia Huang ,
Xin Long ,
Lihong Huang  and
Si Fu
Chuangxia Huang
Affiliation:
School of Mathematics and Statistics, Changsha University of Science and Technology, Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha410114, Hunan, P R China Email: cxiahuang@amss.ac.cnlhhuang@csust.edu.cn
Xin Long
Affiliation:
School of Mathematics and Statistics, Changsha University of Science and Technology, Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha410114, Hunan, P R China Email: cxiahuang@amss.ac.cnlhhuang@csust.edu.cn
Lihong Huang
Affiliation:
School of Mathematics and Statistics, Changsha University of Science and Technology, Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha410114, Hunan, P R China Email: cxiahuang@amss.ac.cnlhhuang@csust.edu.cn
Si Fu
Affiliation:
College of Mathematics and Information Science, Jiangxi Normal University, Jiangxi330022, Nanchang, P R China
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Abstract

Taking into account the effects of patch structure and nonlinear density-dependent mortality terms, we explore a class of almost periodic Nicholson’s blowflies model in this paper. Employing the Lyapunov function method and differential inequality technique, some novel assertions are developed 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 recently published literatures. Particularly, an example and its numerical simulations are arranged to support the proposed approach.

Keywords

Nicholson’s blowflies modelpatch structuredensity-dependent mortality termalmost periodic solutionstability

MSC classification

Primary: 34C25: Periodic solutions
Secondary: 34K13: Periodic solutions
Type
Article
Information
Canadian Mathematical Bulletin , Volume 63 , Issue 2 , June 2020 , pp. 405 - 422
Copyright
© Canadian Mathematical Society 2019

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Footnotes

This work was supported by the National Natural Science Foundation of China (Nos. 11971076, 11861037, 11771059, 51839002), the Scientific Research Fund of Hunan Provincial Education Department (No. 16C0036). Chuangxia Huang and Lihong Huang are the corresponding authors.

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