数学物理学报 ›› 2024, Vol. 44 ›› Issue (4): 994-1011.

• • 上一篇    下一篇

具有无穷分布时滞和反馈控制的周期阶段结构单种群模型

尹瑞霞1,王泽东1,张龙1,2,*()   

  1. 1新疆大学数学与系统科学学院 乌鲁木齐 830017
    2新疆维吾尔自治区应用数学重点实验室 乌鲁木齐 830017
  • 收稿日期:2023-07-03 修回日期:2024-04-25 出版日期:2024-08-26 发布日期:2024-07-26
  • 通讯作者: *张龙, E-mail:longzhang_xj@sohu.com
  • 基金资助:
    新疆维吾尔自治区应用数学重点实验室开放课题(2021D04014);新疆维吾尔自治区天山英才领军人才项目(2023TSYCLJ0054);国家自然科学基金(12261087);国家自然科学基金(12262035);国家自然科学基金(12201540);国家自然科学基金(11861065);新疆维吾尔自治区自然科学基金(2022D01E41);新疆维吾尔自治区高校科研项目(XJEDU2021I002)

A Periodic Stage Structure Single-Population Model with Infinite Delay and Feedback Control

Yin Ruixia1,Wang Zedong1,Zhang Long1,2,*()   

  1. 1College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017
    2The Key Laboratory of Applied Mathematics of Xinjiang Uygur of Xinjiang, Urumqi 830017
  • Received:2023-07-03 Revised:2024-04-25 Online:2024-08-26 Published:2024-07-26
  • Supported by:
    Open Project of Key Laboratory of Applied Mathematics of XinjiangUygur Autonomous Region(2021D04014);Leading Talents of Tianshan Mountains Project in Xinjiang Uygur Autonomous Region(2023TSYCLJ0054);NSFC(12261087);NSFC(12262035);NSFC(12201540);NSFC(11861065);Natural Science Foundation of Xinjiang Province(2022D01E41);Scientific Research Programmes of Colleges in Xinjiang(XJEDU2021I002)

摘要:

该文研究了一类具有无穷分布时滞和反馈控制的周期阶段结构单种群模型. 首先得到了辅助系统-周期阶段结构单种群模型存在唯一全局渐近稳定周期解的充分性判别准则, 其次以积分形式建立了模型持久性和正周期解存在性的充分性判别准则. 最后通过数值模拟演示了文中的理论结果.

关键词: 持久性, 周期解, 无穷分布时滞, 反馈控制, 阶段结构

Abstract:

In this paper, we investigate a periodic stage structure single-population model with infinitely distributed delay and feedback control. Firstly, a sufficient criterion for the existence of a unique globally asymptotically stable periodic solution for the auxiliary system-periodic stage structure single-population model is derived. Secondly, we establish sufficiency criteria on the permanence of the model and the existence of a positive periodic solution in the form of integral. Finally, we illustrate the results with numerical simulations.

Key words: Permanence, Periodic solution, Infinite delay, Feedback control, Stage structure

中图分类号: 

  • O175