两种群植物病虫害模型的正平衡点的稳定性

Stability of the Positive Equilibrium Point of the Model which Contains two Species of Plant Diseases and Insect Pests

考虑了病虫害存在区域内的害虫和植物的关系,根据单位时间内植物在人工喷洒杀虫剂的作用下所呈现的三种状态,建立了一个两种群植物病虫害模型.然后给出了它的唯一正平衡点,利用稳定性第一近似方法讨论了正平衡点的存在性和稳定性.最后利用MATLAB软件进行相应的数值模拟,充分地体现了结论的合理性,最终得出了针对该病虫害模型的最佳解决办法.

This paper considers the relationship between the pests and plants in the area which exists the pests and diseases. According to the three state of plants under the effect of artificial pesticides in a unit of time, we set up a model of two species of plant diseases and insect pests. Then, We have given the unique positive equilibrium point of the model. And by the means of the first approximation method about the stability, we discuss the existence and stability of the equilibrium point. At last, we use Matlab to carry out corresponding numerical simulation, which fully reflects the rationality of conclusion. Finally we have got the best solution about this model of plant diseases and insect pests.