A dynamical analysis of supply chain systems under a dynamic game framework considering green technology innovation

A green supply chain comprising two manufacturers incorporating green technology innovation and one product component supplier was constructed. A green supply chain dynamic model was established based on a gradient adjustment mechanism. The dynamic behavior of the system was analyzed through stability analysis of equilibrium points and bifurcation conditions, combined with parameter continuation methods. One-dimensional bifurcation diagrams, the maximal Lyapunov exponent, and two-dimensional bifurcation diagrams were employed to investigate the system dynamics. The impact of the adjustment speed of green technology innovation levels on the stability of the supply chain dynamic system was discussed. The results indicate that a reasonably set adjustment speed can promote long-term stable operation of the green supply chain for manufacturers. However, excessive adjustment speed may lead the system into an intermittently chaotic state, thereby weakening its disturbance resistance and making it difficult for stability and sustainability to be ensured through existing theoretical frameworks. Under different bifurcation scenarios, the coexistence of multiple periodic transition sequences was observed. The attractors and their basins of attraction were found to vary with changes in the adjustment speed. Border crises were shown to cause grazing interactions between chaotic attractors and the boundaries of adjacent basins, eventually leading to the disappearance of chaotic attractors. These findings may assist green manufacturers in avoiding chaos and reducing potential losses under varying market conditions, and provide theoretical guidance for the timely adjustment of green technology innovation strategies.