害虫胁迫下的棉田能量生态系统稳定性分析  

Stability Analysis on Cotton Field Energy Ecology System with Pest Stress

作　　者：郑立飞[1] 赵鹏[1] 吴养会[1] 赵惠燕[2] ZHENG Li-fei ZHAO Peng WU Yang-hui ZHAO Hui-yan(Institute of Applied Mathematics, Northwest A＆F University, Yangling 712100, China Plant Protection College, Northwest A＆F University, Yangling 712100, China)

机构地区：[1]西北农林科技大学应用数学研究所,陕西杨凌712100 [2]西北农林科技大学植保学院,陕西杨凌712100

出　　处：《数学的实践与认识》2016年第22期186-194,共9页Mathematics in Practice and Theory

基　　金：西北农林科技大学博士科研启动项目资助(2013BSJJ044);西北农林科技大学基本科研业务费专项资金资助(2014YB023;z109021561;2452015086);西北农林科技大学本科优质课程建设项目;国家自然科学基金(39970112;11461024)

摘　　要：在棉田生态系统的基础上研究了以能量为单位的能流数学模型,模型主要包括五个种群:棉株、害虫、捕食性天敌、寄生性天敌以及土壤微生物.基于模型使用微分方程模拟出了能量在各个每个物种之间的流动,并给出了系统的正平衡点存在性和稳定性的条件.最后使用Matlab软件对模型中各个种群的能量变化进行直观的模拟.旨在通过已知的模型在正平衡点处稳定的条件,对棉田生态系统的管理和系统控制提供理论指导.This paper built a mathematical model using energy unit to study the cotton field ecosystem.The model included the five main species：cotton plants,pests,predator species,parasite species and soil microorganism.With differential equations theory,the paper simulated the energy flow among five species,studied the existence of a positive equilibrium point,and obtained the conditions for the existence of positive equilibrium point.Using stability theory to study the stability of the positive equilibrium,this paper explored the stable conditions of positive equilibrium point.Finally,with MATLAB software,the paper gave all parameters value and simulated the result of the model.By discussing known model＇s positive equilibrium point stability,this paper provides theoretical guidance to the cotton fields of ecosystem management and system＇s pest control.

关 键 词：能流分析法 正平衡点 局部渐近稳定性 

分 类 号：O175[理学—数学]