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

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.