具有季节性切换反应及脉冲扰动的鱼类单种群动力学模型

数学物理学报 ›› 2025, Vol. 45 ›› Issue (4): 1206-1216.

具有季节性切换反应及脉冲扰动的鱼类单种群动力学模型

曾夏萍(),卢文雯,庞国萍,梁志清^*()

广西应用数学中心 (玉林师范学院), 广西高校复杂系统优化与大数据处理重点实验室广西玉林 537000

收稿日期:2024-08-12 修回日期:2025-04-14 出版日期:2025-08-26 发布日期:2025-08-01
通讯作者: *E-mail: lzqysl@sohu.com
作者简介:E-mail: xiaping062@163.com
基金资助:
国家自然科学基金(12261096);广西自然科学基金(2024GXNSFBA010395);广西高校中青年教师科研基础能力提升项目(2021KY0592);广西高校中青年教师科研基础能力提升项目(2022KY0582);广西高校中青年教师科研基础能力提升项目(2025KY0675);广西应用数学中心 (玉林师范学院) 开放课题(2023CAM005)

Single Population Dynamics Model of Fish with Seasonal Switching and Impulsive Perturbations

Zeng Xiaping(),Lu Wenwen,Pang Guoping,Liang Zhiqing^*()

Center for Applied Mathematics of Guangxi, Yulin Normal University, Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Guangxi Yulin 537000

Received:2024-08-12 Revised:2025-04-14 Online:2025-08-26 Published:2025-08-01
Supported by:
NSFC(12261096);Natural Science Foundation of Guangxi Grants(2024GXNSFBA010395);Project for enhancing Young and Middle-aged teacher's research basic ability in colleges of Guangxi(2021KY0592);Project for enhancing Young and Middle-aged teacher's research basic ability in colleges of Guangxi(2022KY0582);Project for enhancing Young and Middle-aged teacher's research basic ability in colleges of Guangxi(2025KY0675);Systematic Project of Center for Applied Mathematics of Guangxi(2023CAM005)

摘要/Abstract

摘要：

该文考虑了一类具有季节性切换和脉冲扰动的鱼类单种群模型, 研究季节切换和脉冲扰动对鱼类种群动力学行为的影响. 利用离散动力系统频闪映射理论得到了鱼类单种群系统持久生存和灭绝的充分条件, 结合有理差分方程和不动点理论证明了该系统存在唯一全局吸引的正周期解. 最后, 通过数值模拟来验证结论.

关键词: 脉冲扰动, 持久生存, 季节切换, 周期解

Abstract:

This paper considers a class of single population dynamics models for fish that incorporates seasonal switching and impulsive perturbations. It investigates the effects of these factors on fish population dynamics. By employing the discrete dynamical system theory and stroboscopic mapping, we derive the sufficient conditions for the permanence and extinction of the fish population system. Using rational difference equations and fixed point theory, we demonstrate the existence of a unique globally attractive positive periodic solution. Finally, numerical simulations are provided to validate the theoretical results.

Key words: impulsive disturbance, permanence, seasonal switching, periodic solution

中图分类号:

O175.2

曾夏萍, 卢文雯, 庞国萍, 梁志清. 具有季节性切换反应及脉冲扰动的鱼类单种群动力学模型[J]. 数学物理学报, 2025, 45(4): 1206-1216.

Zeng Xiaping, Lu Wenwen, Pang Guoping, Liang Zhiqing. Single Population Dynamics Model of Fish with Seasonal Switching and Impulsive Perturbations[J]. Acta mathematica scientia,Series A, 2025, 45(4): 1206-1216.

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