Abstract: In view of the first-order difference game model can not effectively reflect the uncertainty of supply chain system and in the process of passing information distortion, a new three-dimensional Supply Chain Fractional order Difference Game Model（SCFDGM） composed of manufacturers, distributors and retailers is proposed. By using the correlation theory of fractional order difference, the numerical experiments are performed to analyze the complex dynamic behavior of SCFDGM, and the effect of the output adjustment speed parameter on the dynamic behavior of the system is discussed. The results show that production adjustment speed is too fast will lead to chaos in the manufactures output decision making, while the distributors and retailers are relatively stable. By using the method of parameter control, the double period bifurcation and unstable periodic orbit of the producer’s production are controlled, and the model of the chaotic model is stabilized to the Nash equilibrium state again. Therefore, SCFDGM provides a theoretical guide for the production, management, decision-making, market rational competition and orderly development of the supply chain system.

Key words: game model, fractional order difference, chaos, chaos control

摘要： 鉴于一阶差分博弈模型不能有效地反映供应链系统的不确定性及在传递过程中的信息扭曲，提出一种新的由生产商、分销商、零售商构成的三维供应链分数阶差分博弈模型（SCFDGM）。利用分数阶差分的相关理论对SCFDGM复杂动力学行为进行数值实验分析，讨论产量调整速度参数对系统动力学行为的影响。结果表明，若生产商产量调整速度过快会使系统进入混沌状态，但同时分销商与零售商则保持相对稳定；采用参数控制的方法对生产商产量决策的倍周期分岔和不稳定周期轨道进行了混沌控制，使陷入混沌的模型重新稳定到Nash均衡状态。因此，SCFDGM为供应链系统企业的生产、管理、决策、市场的合理竞争、有序发展提供了理论指导。

关键词: 博弈模型, 分数阶差分, 混沌, 混沌控制