Dynamic competitive game study of a green supply chain with R&D level

Green and low carbon is an important way to coordinate economic and social development, which is also true for enterprises. Hence, the essay mainly builds up a green supply chain consisting of one supplier and two manufacturers. Gradient adjustment mechanism is used to establish a dynamic green competition model based on bounded rationality in this paper. Subsequently, the stability of four equilibrium points is researched through different methods. Dynamic behaviors are analyzed by 1-D bifurcation diagrams, the largest Lyapunov exponent, as well as 2-D bifurcation diagrams. We have found that the system goes from a steady state to chaos mainly via flip bifurcation. The chaotic state of system can be alleviated as the increase of adjustment speed in a certain range. Furthermore, invariant sets and natural transverse Lyapunov exponent are used to study synchronization behavior. Basins of attraction under the coexistence of attractors are simulated numerically. The results indicate that the system will have two and four groups of coexisting attractors, where the structure and size of the attractor and its basin will change as the speed of adjustment increases. When the attractor contacts with the boundary of its basin of attraction, the global bifurcation occurs.