棉田生态系统时滞动力学模型及其应用  

Delay Differential Equations and Application in Cotton Ecosystem

作　　者：郑立飞[1] 陈小蕾[1] 张良[1] 杨秀香[2] 万阿英 ZHENG Li-feil;CHEN Xiao-lei;ZHANG Liang;YANG Xiu-xiang;WAN A-ying(College of Science,Northwest A&F University,Yangling 712100,China;College of Mathematics and Information Science,Weinan Normal University,Weinan 714000,China;School of Mathematics and Statistics,Hulunbeir College,Hailar 021008,China)

机构地区：[1]西北农林科技大学理学院,陕西杨凌712100 [2]渭南师范学院数学科学学院,陕西渭南714000 [3]呼伦贝尔学院数学与统计学院,内蒙古海拉尔021008

出　　处：《数学的实践与认识》2024年第1期246-256,共11页Mathematics in Practice and Theory

基　　金：内蒙古自治区自然科学基金(2018MS01023);国家自然科学基金项目(11461024);陕西省自然科学基础研究计划(2020JM-175);西北农林科技大学教学改革项目(JY1902013)。

摘　　要：以棉田生态系统能量流动分析为基础,建立了作物-害虫-天敌-微生物的时滞种群动力学模型,利用泛函微分方程理论对该系统进行了持久性和稳定性研究,对系统解的正性、持久性、正平衡点的存在性及全局渐近稳定性给出了相关条件,证明该系统的时滞是无害时滞.最后使用MATLAB软件对模型进行了动态模拟,对正平衡点的存在性条件和稳定性进行了验证.This study built delay differential equations on crop-pest-natural enemy-soil mi-croorganism using energy unit of cotton ecosystem and analysis it with the theory of functional differential equations.The result shows that this system is permanent and all solutions are positive.And it has unique positive equilibrium point which is global asymptotically stable under some conditions.Other more,two delays in this system are harmless,which means this system in cotton ecosystem could be not considered delays or developmental period of crop,pest and natural enemy.Lastly,Matlab software was used to simulate this system and verified the right of above results.

关 键 词：无害时滞 种群动力学 能量转化 时滞微分方程 

分 类 号：O175[理学—数学] S562[理学—基础数学] S181[农业科学—作物学]