Abstract: Based on quantum game theory and classical game theory, a quantum Cournot dynamics model considering spillover effect is constructed by applying Li-Du-Masser quantization scheme and introducing quantum entanglement parameters. The stability of Nash equilibrium point and boundary equilibrium point is analyzed by Jury criterion and Jacobi matrix, Matlab is applied to carry out numerical simulation to study the influence of parameter changes on the stability domain of the system, and the coexistence, local and global bifurcation phenomena in the model are analyzed, and the results show that smaller adjustment speed is more conducive to the stability of the market, and the small change of entanglement parameter will lead to the occurrence of the system’s global and local bifurcation, and reasonable control of the spillover effect parameter, the degree of entanglement and the adjustment speed is more conducive to the stability of the system.