双渠道供应链中时滞价格博弈模型的稳定性分析

Stability Analysis of Price Game Model with Delay in Dual-channel Supply Chain

建立了双渠道供应链中带时滞的微分价格博弈模型,以零售商的延迟决策作为时滞参数,通过特征值法分析了模型Hopf分岔的存在性及其在平衡点处的局部渐近稳定性,给出了模型分岔的时滞参数临界点。数值仿真验证了理论分析的正确性,并分别探究了渠道替代度和产品质量对价格和利润的影响。研究表明,时滞参数必须保持在一定的范围内,否则系统会失稳;渠道替代度和产品质量存在最优值;延迟反馈控制法能够对失稳系统进行有效控制,使其重返稳定状态。

A differential price game model with delay in a dual-channel supply chain is established. The delay decision of the retailer is taken as a delay parameter. The existence of the Hopf bifurcation and the local asymptotic stability at the equilibri-um point are analyzed by the eigenvalue method. The bifurcation critical point of the delay parameter of the model is given. The correctness of theoretical analysis is verified by numerical simulation, and the inffluence of channel substitution degree and prod-uct quality on price and profit is explored respectively. The study shows that the delay parameters must be kept in a certain range, otherwise the system will be unstable, the channel substitution degree and the product quality have the optimal value, and the delay feedback control method can effectively control the instability system and ensure its stability.