Abstract: This paper presents a R&D duopoly investment competition model with incomplete information，and analyzes the stability of the Nash equilibrium with economic meaning.Then existence of the model’s Hopf bifurcation is also studied.At last，the direction and stability of the bifurcation are analyzed by computing the first Lyapunov exponent，and the corresponding numerical simulations are presented.

摘要： 提出了一个双寡头R&D投资竞赛的非线性动力学离散模型，接着对该模型中有经济意义的Nash均衡点的稳定性以及其Hopf分岔的存在性进行了分析。最后通过计算第一Lyapunov指数，对模型产生的Hopf分岔的方向与稳定性进行了计算和证明，并进行了仿真模拟。