中文摘要：

利用非线性动力系统的分支理论，研究了分别具有有限理性和简单理性的双寡头R＆D竞争模型，通过对模型的解析分析和数值仿真，研究了技术溢出对双寡头R＆D竞争演化的影响。结果表明：技术溢出对系统均衡点的存在性、均衡点的个数、均衡点的取值以及均衡点的稳定性、系统稳定区域都有显著的影响；技术溢出对双寡头的R＆D平均投入、平均利润也有显著影响，具体的影响规律随着系统所处的状态不同而有所变化；同时，系统竞争过程还表现出对技术溢出具有敏感依赖性的特征。

英文摘要：

By using the theory of bifurcations of dynamical systems, the model of R＆D competition in duopoly with heterogeneous rationality is constructed, and the impact of technology spillovers on duopoly＇s R＆D competition is discussed. Analysis and simulation results show that technology spillovers have obvious impact on the existence, quantity, value and stability of the equilibrium point and the extension of equilibrium area. Technology spillovers influence differently on average R~D input and average profits when the system is in different states. Technology spillovers have impressible influence on R＆D competition model.