生产周期和更新换代影响下的商品微分动力模型分析  

Analysis of commodity differential dynamic model based on production cycle and renewal superposition effect

作　　者：高德宝[1] 魏玉芬[1] 朱焕[1] GAO De-bao;WEI Yu-fen;ZHU Huan(College of Science,Heilongjiang August First Agricultral University,Daqing 163319,China)

机构地区：[1]黑龙江八一农垦大学理学院,黑龙江大庆163319

出　　处：《高校应用数学学报（A辑）》2021年第4期411-422,共12页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：黑龙江省哲学社会科学规划(19SHE281);大庆市指导性科技计划(zd-2020-63)。

摘　　要：多数商品需要生产时间,为了增加市场竞争力,它们更需要更新换代.基于生产周期和更新换代对商品需求量,价格和供给量的内在影响,利用微分动力学的相关理论建立两个商品微分动力学模型.对模型进行定性分析得出一些与实际情况相吻合的结论.当商品仅受生产周期影响时,不同条件下,需求量,价格和供给量会稳定地收敛于正平衡点或围绕正平衡点作周期性波动.在生产周期和更新换代叠加效应影响下,需求量,价格和供给量均有上限并且在某一时刻后,三者均会作周期性波动.最后,用数值仿真验证相关结论的正确性.Production time is indispensable to most commodities which need more upgrading for increasing market competitiveness.Based on the internal influence of production cycle and upgrading on the demand,price and supply of commodities,two differential dynamics models of commodities are established by using the relevant theory of differential dynamics.Some conclusions are drawn through qualitative analysis of the model which are consistent with the actual situation.When the commodity is only affected by the production cycle,the demand,price and supply will converge to the positive equilibrium or fluctuate periodically around the positive equilibrium under different conditions.Under the superimposed effect of production cycle and replacement,demand,price and supply are all capped and fluctuate periodically after a certain point.Finally,numerical simulation is used to verify the correctness of the relevant conclusions.

关 键 词：生产周期 更新换代 平衡点 稳定性 数值仿真 

分 类 号：O175.14[理学—数学] F016[理学—基础数学]