Hopf Bifurcation Analysis in a Modified R&D Model with Delay

We consider a duopoly game model of R&D (research and development) rivalry between two high-tech firms with time delay, in which a monopoly sector with R&D spillover is studied using a mixture of game theory and nonlinear dynamics theory. The local asymptotic stability of the equilibrium point is studied by analyzing the corresponding characteristic equation. It is found that the delay can lead the system dynamic behavior to exhibit stability switches and Hopf bifurcations appear.