Stability and Complexity Analysis of Multichannel Supply Chain with Price Competition

The multichannel sales mode is employed by more and more manufacturers to maximize their profits or gain much more than market share. This paper develops a dynamic pricing game model of multichannel supply chain, and focuses on the impacts of channel competition on the complex characteristics of the evolutionary dynamic game, using analyses based on stability domain, bifurcation diagram, the largest Lyapunov exponent, attractor domain and time series. The results indicate that the system will gradually enter chaotic state through flip bifurcation from stable state with the increase of price adjustment speed, and the two-dimensional stability domain will shrink as the competition coefficient increases. Interestingly, although an increase in commission rate will lead to a decrease in profits, it will widen the stability range of the whole system. In the end, for further analysis, the chaotic behavior of the multichannel supply chain is controlled by using the feedback control method. The manufacturer is suggested to adopt a cautious pricing strategy in the stability region, and minimize the direct competition between channels in the sales process and diversify the productions in different channels.