直接离散Verhulst模型构建及其优化  

Construction and Optimization of Direct Discrete Verhulst Model

作　　者：罗友洪 陈友军[1] Luo Youhong;Chen Youjun(School of Mathematics and Information,China West Normal University,Nanchong Sichuan 637002,China)

机构地区：[1]西华师范大学数学与信息学院,四川南充637002

出　　处：《统计与决策》2021年第14期24-28,共5页Statistics & Decision

基　　金：西华师范大学英才科研基金项目(17YC370);西华师范大学教学改革与研究重点项目(jgxmzd1824)。

摘　　要：针对Verhulst离散模型与白化方程之间联系不紧密,以及模型适用范围存在局限性等问题,文章以散Verhulst模型动态建模求解出参数,再对参数求均值,并将参数的均值还原后代入Verhulst直接建模模型时间响应式,结果表明,直接离散Verhulst模型能够100%模拟指数型序列与饱和S型序列。最后通过实例验证了直接离散Verhulst模型可以进行模拟、短期预测与长期预测。In view of the lack of close connection between Verhulst discrete model and whitening equation as well as the limitation of model application scope,this paper is based on the solution of the whitening differential equation of the Verhulst direct modeling model to deduce the direct discrete Verhulst model,and then uses the least square method to solve the parameters by dynamic modeling for the direct discrete Verhulst model,with the mean value of the parameters calculated.Finally,the paper restores the mean value of the parameters and puts it into the time response formula of Verhulst direct modeling model.The results show that the direct discrete Verhulst model can simulate both exponential series and saturated S-type series 100%.The paper also gives an example to verify that the direct discrete Verhulst model can be used for simulation,short-term prediction and long-term prediction.

关 键 词：Vrhulst模型 直接离散 动态优化 适用性 

分 类 号：C81[社会学—统计学]