Abstract
In this paper, a dynamical Cournot model with nonlinear demand and R&D spillovers is established. The system is symmetric when the duopoly firms have same economic environments, and it is proved that both the diagonal and the coordinate axes are the one-dimensional invariant manifolds of system. The results show that Milnor attractor of system can be found through calculating the transverse Lyapunov exponents. The synchronization phenomenon is verified through basins of attraction. The effects of adjusting speed and R&D spillovers on the dynamical behaviors of the system are discussed. The topological structures of basins of attraction are analyzed through critical curves, and the evolution process of “holes” in the feasible region is numerically simulated. In addition, various global bifurcation behaviors, such as two kinds of contact bifurcation and the blowout bifurcation, are shown.
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
