一类具有时滞的小麦病虫害传播模型的研究与稳定性分析

Research and Stability Analysis for a Class of Delayed Propagation Model of Wheat Diseases and Pests

针对小麦病虫害无病平衡点存在不稳定性的问题。提出一类基于时滞二自由度的小麦病虫害传播模型,从2012-2014年对驻马店市小麦上发生的病虫害种类、为害程度进行了统计,进行模型数据的筛选,利用小麦虫害统计结果中的虫害7种,天敌种类12种,小可引起疾病的原因12种。利用麦蚜、麦红吸浆虫、麦蜘蛛等虫害的统计结果带入时滞二自由度控制数学模型,得到稳定的结果。实验统计结果说明,该控制模型对小麦病虫害传播的数学建模过程较为成功,抑制了病虫害的传播行为,降低被感染概率。

In view of the wheat plant diseases and insect pests disease- free equilibrium problems of instability. Proposed a class of plant diseases and insect pests of wheat spread model based on time delay two degree of freedom, from 2012 to 2014 in zhumadian wheat on the kinds of diseases and insect pests,degree of harm to the statistics, to model data filtering, and by using the statistical results of seven wheat insect pests and natural enemy species 12, xiaoke cause disease of 12. Using wheat aphid, Mai Gong suck pulp, wheat spider insect pests of statistical results into delay two degree of freedom control mathematical model of stable results are obtained. The experiment statistical result shows that the mathematical modeling process control model for the spread of diseases and insect pests of wheat more successful, inhibit the spread of diseases and insect pests, reduce the probability of infection.