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

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

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 Long^1,^2,^*()

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/Abstract

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

尹瑞霞, 王泽东, 张龙. 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[J]. 数学物理学报, 2024, 44(4): 994-1011.

Yin Ruixia, Wang Zedong, Zhang Long. A Periodic Stage Structure Single-Population Model with Infinite Delay and Feedback Control[J]. Acta mathematica scientia,Series A, 2024, 44(4): 994-1011.

图/表 4

参考文献 25

[1]	Vance R R, Coddington E A. A nonautonomous model of population growth. J Math Biol, 1989, 27(5): 491-506 pmid: 2794800
[2]	Chen F D, Yang J H, Chen L J. Note on the persistent property of a feedback control system with delays. Nonlinear Anal: Real World Appl, 2010, 11(2): 1061-1066
[3]	Liu S Q, Chen L S, Agarwal R. Recent progress on stage-structured population dynamics. Math Comput Model, 2002, 36: 1319-1460
[4]	Cui J A, Chen L S, Wang W D. The effect of dispersal on population growth with stage-structure. Comput Math Appl, 2000, 39(1/2): 91-102
[5]	Wang C Y, Li L R, Zhang Q Y. Dynamical behaviour of a Lotka-Volterra competitive-competitive-cooperative model with feedback controls and time delays. J Biol Dyn, 2019, 13(1): 43-68
[6]	Gopalsamy K, Weng P X. Feedback regulation of logistic growth. Internat J Math Sci, 1993, 16(1): 177-192
[7]	Jana S, Kar T K. A mathematical study of a prey-predator model in relevance to pest control. Nonlinear Dyn, 2013, 74: 667-683
[8]	傅金波, 陈兰荪. 基于生态环境和反馈控制的多种群竞争系统的正周期解. 数学物理学报, 2017, 37A(3): 553-561
	Fu J B, Chen L S. Positive periodic solution of multiple species comptition system with ecological environment and feedback controls. Acta Math Sci, 2017, 37A(3): 553-561
[9]	Basir F A, Noor M H. A model for pest control using integrated approach: Impact of latent and gestation delays. Nonlinear Dyn, 2022, 108(2): 1805-1820
[10]	Teng Z D, Chen L S. Permanence and extinction of periodic predator-prey systems in a patchy environment with delay. Nonlinear Anal: Real World Appl, 2003, 4(2): 335-364
[11]	Pu L Q, Adam B, Lin Z Q. Extinction in a nonautonomous competitive system with toxic substance and feedback control. J Appl Anal Comput, 2019, 9(5): 1838-1854
[12]	Chen F D, Li Z, Huang Y J. Note on the permanence of a competitive system with infinite delay and feedback controls. Nonlinear Anal: Real World Appl, 2007, 8(2): 680-687
[13]	Guo K, Song K Y, Ma W B. Existence of positive periodic solutions of a delayed periodic Microcystins degradation model with nonlinear functional responses. Appl Math Lett, 2022, 131: 108056
[14]	王长有, 李楠, 蒋涛, 杨强. 一类具有时滞及反馈控制的非自治非线性比率依赖食物链模型. 数学物理学报, 2022, 42A(1): 245-268
	Wang C Y, Li N, Jiang T, Yang Q. On a Nonlinear non-autonomous ratio-dependent food chain model with delays and feedback controls. Acta Math Sci, 2022, 42A(1): 245-268
[15]	Shi L, Qi L X, Zhai S L. Periodic and almost periodic solutions for a non-autonomous respiratory disease model with a lag effect. Acta Math Sci, 2022, 42B(1): 187-211
[16]	Zhang L, Teng Z D. Permanence for a delayed periodic predator-prey model with prey dispersal in multi-patches and predator density-independent. J Math Anal Appl, 2008, 338(1): 175-193
[17]	Hu H X, Teng Z D, Jiang H J. Permanence of the nonautonomous competitive systems with infinite delay and feedback controls. Nonlinear Anal: Real World Appl, 2009, 10(4): 2420-2433
[18]	Liu Z Q, Kang S M. Applications of Schauder's fixed-point theorem with respect to iterated functional equations. Appl Math Lett, 2001, 14(8): 955-962
[19]	张恭庆, 林源渠. 泛函分析讲义. 北京: 北京大学出版社, 2004
	Zhang G Q, Lin Y Q. Lecture Notes on Functional Analysis. Beijing: Peking University Press, 2004
[20]	Hale J K. Introduction to Functional Differential Equations. New York: Springer, 1993
[21]	Smith H L. Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems. Providence, RI: American Mathematical Society, 1995
[22]	滕志东, 陈兰荪. 高维时滞周期的 Kolmogorov 型系统的正周期解. 应用数学学报, 1999, 22(3): 446-456 doi: 10.12387/C1999072
	Teng Z D, Chen L S. The positive periodic solutions of periodic Kolmogorov type systems with delays. Acta Math Appl Sin, 1999, 22(3): 446-456 doi: 10.12387/C1999072
[23]	Wu H, Chen W, Wang N, et al. A delayed stage-structure brucellosis model with interaction among seasonality, time-varying incubation and density-dependent growth. Int J Biomath, 2023, 16(6): 2250114
[24]	Pandey S, Ghosh U, Das D, et al. Rich dynamics of a delay-induced stage-structure prey-predator model with cooperative behaviour in both species and the impact of prey refuge. Math Comput Simul, 2024, 216: 49-76
[25]	Hu D P, Li Y Y, Liu M, et al. Stability and Hopf bifurcation for a delayed predator-prey model with stage structure for prey and Ivlev-type functional response. Nonlinear Dynam, 2020, 99: 3323-3350