The complex dynamics of R&D competition models of three oligarchs with heterogeneous players

Abstract

This paper uses the theory of bifurcations of dynamical systems, considering R&D input competition model in oligopoly market with heterogeneous rationality. We assume that cooperation, as well as competition, exists among the oligarchs, which are closer to reality and different from previous studies. On the basis of analyzing the stabilities of four fixed points in the three-dimensional dynamic system, a local stable region of Nash equilibrium is obtained. Simulation results show that the adjustment of R&D input speed has an obvious impact on the complexity of competition, and also show that the system profit will decrease when it is in chaos. So this paper discusses the application of parameters control method when the model is in chaos and then allows the oligarchs to eliminate the negative effects.