一类蚜虫种群突变模型的建立与实证分析

Establishment and empirical analysis of a class of aphid populations catastrophe model

基于调查资料及气象数据,绘制相应的散点图,用其分析蚜虫种群动态并建立尖角突变模型.利用回归分析方法和SPSS软件,确定模型中的正则变量和剖分变量.根据显著性检验,将线性模型、Logistic模型与尖角突变模型做比较,其结果显示尖角突变模型有更好的拟合度.最后,根据突变理论对模型的平衡点和稳定性进行分析,结果可为蚜虫种群的预测预报提供参考.

Based on the investigation and meteorology data, the corresponding scatterplot is drawn. And then the dynamics of aphid populations is analyzed and the cusp catastrophe model is proposed. Using the regression analysis and SPSS software,the regular variable and the split variable of the model are determined.By comparing linear model, Logistic model with cusp catastrophe model, the result shows that the cusp catastrophe model has more fitting degree. Finally, equilibrium and stability of the model analysis is studied by catastrophe theory, the result may provide the reference for the prediction and forecast of aphid populations.