<p>The pervasive integration of the Internet alongside heightened consumer emphasis on environmental sustainability has catalyzed the expansion of direct sales channels by manufacturers. Against this backdrop, the dual-channel supply chain has emerged as the predominant distribution model within the industry. This research develops a Stackelberg dynamic model, innovatively applying chaos theory to examine the role of consumer environmental awareness. The study scrutinizes the complexities of pricing strategies and investigates the stability of the equilibrium state in the corresponding discrete dynamic system. Through numerical simulations, this paper analyzes the impact of adjustment parameters and consumer preferences on the dynamics of the system. The findings are manifold: Firstly, the direct price adjustment parameter by the manufacturer exerts the most significant influence on the system’s stability. Secondly, an increase in this parameter leads to a transition from stability to chaos, adversely affecting the manufacturer’s profits while benefiting the retailer, particularly under decentralized decision-making scenarios. Thirdly, a rising consumer predilection for eco-friendly products encourages manufacturers to enhance their environmental safeguards, potentially boosting their profits, albeit with minimal impact on retailer earnings. This investigation provides a theoretical framework for understanding how consumer preferences can guide optimal decision-making for entities within a dual-channel supply chain.</p>