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In this paper, we study a dual-channel closed-loop supply chain in which a manufacturer considers the market waste products recovery and remanufacture, and a retailer considers provide services to customers. We build a Stackelberg game model and a centralized game model in a static and dynamic state, respectively, and analyze the two dynamic models by mathematical analysis and explore the stability and entropy of the two models using bifurcation, the basin of attraction, chaotic attractors, and so on. The influences of service level and profit distribution rate on the system's profit are discussed. The theoretical results show that higher price adjustment speed will lead to the system lose stability with a larger entropy value. In the Stackelberg game model, the stability of the system increases as the service value and the recovery rate increases; in the centralized model, the stability of the system decreases with the increase of the service value and increases with the recovery rate increases. When the Stackelberg game model is in a stable state, the manufacturer's profit increases first and then decreases, and the retailer's profit first decreases and then increases as the service value of the retailer increases. The research will serve as good guidance for both the manufacturer and retailer in dual-channel closed-loop supply chains to improve decision making.

The Complexity Entropy Analysis of a Supply Chain System Considering Recovery Rate and Channel Service