In this paper, we study a dual-channel closed-loop supply chain (CLSC) consisting of one manufacturer, one retailer and one third-party firm or platform (3P). The manufacturer wholesales new products through the traditional retail channel and distributes remanufactured products via 3P. We focus on establishing the dynamic Stackelberg game models for nondelayed and delayed cases, respectively. The existence and local stability of Nash equilibrium are examined as well as the complex dynamical behaviors of each model under various scenarios are investigated by numerical simulations, such as stability region, bifurcations, chaos, strange attractors, and so on. Moreover, the impacts of some key parameters on the performance of chain members are analyzed. In addition, the variable feedback control method is utilized to eliminate the system chaos. The results reveal that the high value of the consumer discount perception for remanufactured products and excessively fast price adjustment speed have a destabilization effect on the Nash equilibrium point. In addition, adopting delay decisions by manufacturer does not always make the system more stable because it can exert either positive or negative effect on the system’s stability, while an intermediate delay weight is conducive to the system have a higher chance to stay stable. Furthermore, the manufacturer’s profits will be declined significantly while the profits of retailer and 3P will be elevated to some extent when the system falls into periodic and chaotic motions, so chaos is not always necessarily detrimental to all the decision makers in the dual-channel CLSC.
This paper considers a two-echelon supply chain consisting of one government, one manufacturer and one retailer in the presence of government green subsidies and carbon cap-and-trade policies. The manufacturer adopts eco-friendly technologies to produce green products for curbing carbon emissions, and the retailer is responsible for selling green products to consumers who exhibit low-carbon preferences. Two noncooperative game models, that is, the manufacturer-led Stackelberg model and the vertical Nash model, are developed under static and dynamic settings, respectively. The static analytical solutions of the models are derived by using game theory, and their complex dynamical behaviors are explored via bifurcation and chaos theory. The results indicate that the excessively large adjustment parameters of the players will destabilize the stability of the Nash equilibrium point, leading to more complicated behaviors such as bifurcation and chaos. The higher consumers’ low-carbon preference has a destabilization effect on the system’s stability while the carbon trading price may be a stabilizing or a destabilizing factor for the system under different scenarios. Besides, the influence of the government’s green subsidy rate on the system’s stability is not obvious in most cases. Furthermore, when the system enters into periodic cycles and chaotic motions resulting from the overly fast adjustment speeds, the channel members’ performance may be elevating or declining in different models. Therefore, the chaos in the low-carbon supply system is not always detrimental to the channel members.
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