中文摘要：

将牛鞭效应的形成过程描述成系统内部的非线性机制，并应用非线性理论对牛鞭效应的产生机理进行了深入研究．研究结果表明，牛鞭效应与“蝴蝶效应”具有同样的自激放大机制．在受到零售商需求信息处理偏差的扰动下．供应商的订货决策会自激放大这些扰动．同时，制造商的周期性低价促销，也会使零售商的订货决策随产品价格的波动而自激放大产品需求，形成牛鞭效应．这种需求变异放大现象的外在表现则是系统对初始值敏感依赖的非线性机制作用下出现的系统自相似结构．为此，本文采用G-P算法计算得到需求信息处理和价格波动下牛鞭效应的关联维数．结果表明，需求信息处理和价格波动下牛鞭效应具有分形特征．

英文摘要：

This paper describes the forming process of the bullwhip effect as the internal nonlinear mechanism and applies the nonlinear theory in the research on the mechanism of bullwhip effect. Research shows that bullwhip effect and butterfly effect posses the same the self-oscillation amplifying mechanism, that is, the ordering decisions of the supplier can self-oscillatoryly amplify the perturbations brought by the errors in the processing of retailers＇ demand information. Meanwhile, producers＇ seasonal promotions at low price also lead the occurrence of bullwhip effect, namely retailers＇ ordering decisions will self-oscillatoryly amplify the demand with the price variation. This results show an explicit self-similar structure of the sensitivity of the system to the initial values duty to the nonlinear mechanism. This paper applies the G-P algorithm to calculate the relativity dimension under the demand information processing and price changing, the results show that the bullwhip effect under demand signal processing and price variations possesses the fractal feature.