加权分数阶离散Verhulst模型及其应用  

Weighted Fractional Discrete Verhulst Model and Its Application

作　　者：石莹莹 朱锋 周陈裕 王建宏[1] SHI Ying-ying;ZHU Feng;ZHOU Chen-yu;WANG Jian-hong(School of Mathematics and Statistics Sciences,Nantong University,Nantong 226019,China)

机构地区：[1]南通大学数学与统计学院,江苏南通226019

出　　处：《数学的实践与认识》2024年第3期76-87,共12页Mathematics in Practice and Theory

基　　金：全国统计科学研究项目(2020LY020);南通市科技计划项目(MS12021058)。

摘　　要：为了提高传统Verhulst模型的拟合和预测精度,文章根据新信息优先原理,采用加权累加和加权累减的信息处理方式,建立基于加权分数阶累加生成的离散Verhulst模型.采用河北省的年末人口数进行预测,将新建模型与传统Verhulst模型和分数阶离散Verhulst模型进行比较.结果显示,加权分数阶离散Verhulst模型具有较高的精度和较强的稳定性,具有一定的实用价值.In order to improve the fitting and prediction accuracy of the traditional Verhulst model,the article adopts the information processing method of weighted accumulation and weighted reducing according to the new information priority principle,and establishes a discrete Verhulst model based on weighted fractional accumulation.The population at the end of the year in Hebei Province is adopted.Make predictions and compare the new model with the traditional Verhulst model and the fractional discrete Verhulst model.The results show that the weighted fractional discrete Verhulst model has high accuracy and strong stability,and has certain practical value.

关 键 词：加权累加 分数阶 离散Verhulst模型 人口预测 

分 类 号：N941.5[自然科学总论—系统科学]