产品销售网络动力学建模

王佩秋; 靳祯; 陈华

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产品销售网络动力学建模

自动化与计算机技术 | 更新时间：2026-09-14

- 产品销售网络动力学建模
- Dynamic Modeling on Production Marketing Network
- 中北大学学报（自然科学版） 2013年34卷第2期页码：147-152
- 作者机构：
  
  中北大学理学院
- 作者简介：
- 基金信息：
  
  国家自然科学基金资助项目(11171314)
- DOI：
  中图分类号：
- 纸质出版：2013
- 稿件说明：
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王佩秋, 靳祯, 陈华. 产品销售网络动力学建模[J]. 中北大学学报（自然科学版）, 2013,34(2):147-152.

王佩秋, 靳祯, 陈华. Dynamic Modeling on Production Marketing Network[J]. 2013, 34(2): 147-152.
王佩秋, 靳祯, 陈华. 产品销售网络动力学建模[J]. 中北大学学报（自然科学版）, 2013,34(2):147-152. DOI：

王佩秋, 靳祯, 陈华. Dynamic Modeling on Production Marketing Network[J]. 2013, 34(2): 147-152. DOI：

摘要

根据个性化推荐系统中建立的用户-产品的二部图

研究了不同品牌产品的用户数量的变化情况

建立了n+1维的关于产品中不同品牌的用户数量变化的动力学模型

并对此进行了数值模拟

得到了系统趋于稳态的结论.在一类产品和两个用户的情况下对模型进行了简化

并对其进行了动力学分析.首先证明了平衡点的唯一存在性

然后进一步证明了平衡点的局部渐近稳定以及通过构造Dulac函数证明了无极限环

进而得到了平衡点全局渐进稳定.

Abstract

According to the user-product bipartite graph of the personalized recommendation system

the changes in the number of users who used different brand of product was investigated

and then a n+1 asymmetric dynamical model was established to describe that change.After simulating

it draws the conclusion that the system can be stable.The model was simplified under the condition of only one product and two users

and we continued to make the dynamic analysis.First

the unique existence of the positive equilibrium was proved

and then its local asymptotic stability was testified and Dulac Function was constructed.Finally

we obtained that there was no limit circle and the positive equilibrium was global asymptotic stable.

关键词

Keywords

references

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