By using the theory of bifurcations of dynamical systems,
the model of R&D competition in duopoly with heterogeneous rationality is
investigated, and the existence and stability of the equilibrium point of
this model are discussed. Simulation results show that the amount of
equilibrium point in practice may be less than in theory, the Nash
equilibrium point is the only equilibrium point of the model, and the speed
of R&D input adjustment has an obvious impact on the results of R&D
competition. Nash equilibrium of R&D competition model can be to
maintainable by using delayed feedback control method when the model in
chaos state.