Complex dynamics of R&D competition with one-way spillover based on intellectual property protection

Abstract

In order to study the R&D competition with one-way spillover based on intellectual property protection, a R&D-Cournot duopoly game between a foreign-invested enterprise and a domestic-invested enterprise is set up in this paper. It is discussed the local stabilities near all the equilibrium points, and it is diplayed the stability conditions of each equilibrium point. Regarding the dynamical behaviors of the model, we mainly carry out our research from two aspects. The first issue we concerned about is the dynamical behaviors when there is only one enterprise engaged in R&D. We found that the coordinate axes are invariant sets, on which the dynamical behaviors are governed by two different one-dimensional maps. The dynamical behaviors of both enterprises engaged in R&D is another topic of our research. We find that not only the local bifurcations can cause the sudden change of dynamics, but also the global bifurcations can lead to the “death” of attractors or the disappearance of coexistence of multiple attractors. Moreover, the stability exchange between different attractors caused by the transcritical bifurcation is also common in our model. The stability and evolutionary pattern of the kinetic evolutionary behavior revealed with the change of the adjustment parameters is closely related to the long-term effects of strengthening intellectual property protection. It is of high practical value to study the impact of intellectual property protection intensity on R&D investment of high-tech enterprises.