Nowadays, with global scientific and technological levels rapidly improving, innovation has been a great need for enterprises to solve the dilemma. Combined with EPR (Extended Producer Responsibility) and the topic of remanufacturer, adopting green innovation has been an effective way when green supply chain management is applied. In this paper, we focus on the activity of green innovation and build a model where the manufacturer will invest in green innovation to improve the product availability rate of recycled products and save the cost in the process of remanufacturing. Besides, we take three stages in a cycle into consideration, that is, production/sale, recycling used production, and remanufacture/sale, and meanwhile, the government gives a subsidy to enterprises to encourage the activity of recycling. In the process of model solving, we take a dynamic decision-making way into consideration. We find that the decision adjustment speed of players has a significant effect on the stability, and in a long dynamic repeated game process, with the speed of decision adjustment increasing, the system enters into chaos at the end of the process. It is interesting that when the speed of decision adjustment exceeds the critical point of the bifurcation diagram, the profit of the manufacturer decreases and then enters a chaotic state. Besides, with the level of subsidies increasing, the area of stable region decreases gradually. Certain investment has a positive effect on product selling and recycling as well as the profit, and the government subsidy undoubtedly raises the profit of manufacturers and encourages the activity of recycling. In the end, we make chaos control by adjusting the decision method.

This study investigates the dynamic game behaviors of dual-channel supply chains involving an oligopoly manufacturer selling low-carbon products to online and offline retailers. The price game models under government subsidy are discussed under three scenarios: (1) simultaneous decision, (2) manufacturer dominates the market, and (3) retailer dominates the market. The equilibrium strategies are compared under the government subsidy policy. Using numerical simulation,complex characteristics of the dual-channel supply chain under the carbon subsidy policy are investigated. The complexity of wholesale price and sales commission of each channel are analyzed by bifurcation, largest Lyapunov exponent and basin of attraction diagrams. Furthermore,parameter adjustment and delayed feedback control methods are proven to be effective approaches to chaos control.