Bifurcation, Global Dynamics And Synchronization In A Bertrand Game With R&D Spillover And Semi-Collusion

In this paper, the local and global dynamics of a two-stage Bertrand dynamic duopoly model with R&D spillover are studied. This paper aims to study the complex dynamics of the built model by changing the speed of adjustment and other parameters. Combining analysis tools and numerical techniques, we discuss the stability of the system and calculate the stability conditions at first. Then we infer the dynamic phenomena of the system with different sets of parameters and get some interesting results. If two firms operate under different market environment, the system will exhibit two kinds of chaotic intermittent phenomena. While if they operate in same market environment, the system will exhibit the synchronization and on-off intermittency. Finally, through the study of complex basins and multistability, we see how the number of attractors and the size or shape of the basin will change with the change of parameters.