中文摘要：

应用非线性动力系统中的分岔和混沌理论及相关的经济学理论，建立了同质三寡头R＆amp;D（研究与开发）竞争在有限理性预期下的动力学模型，分析了该系统的均衡点及其稳定性，并以投入调整速度及技术溢出水平为控制参数，分析了系统产生分岔及混沌状态的条件，进一步得到了寡头间博弈引起的利润变化性态；结合Mathematics对不同参数条件下的系统进行了数值模拟，发现当企业的R＆amp;D投入调整速度过大时，系统由稳定状态进入倍周期分岔进而进入混沌状态；随着企业的技术溢出水平增大，其自身的利润下降，竞争对手的利润上升。模拟结果表明企业的利润在稳定状态下是稳定变化的，在混沌状态下则是连续波动的；当企业的投入调整速度过大时，其自身的平均利润呈下降趋势，竞争对手的平均利润呈上升趋势。

英文摘要：

We apply the theory of bifurcation and chaos of nonlinear dynamical systems and related theory of economics, and then establish a R＆D competition dynamic model under the limited rational expectations of three homogeneous oligarchs and analyze this system′s equilibriums and their stability. We also take adjusting speed of R＆D input and technical spillovers level as the control parameter and analyze the condition of the system bifurcation and chaos, then we get the changing behavior of profit as competition among oligarchs; Under the condition of different parameters we simulate the system by Mathematics and illustrate the result. We find that when the adjusting speed of R＆D input of the enterprise is too large, then the system becomes from stable state into period-doubling bifurcation and chaotic state. As the technical spillovers level of the enterprise increases, its profit falls and the opponent′s profit rises. In addition, the results of simulation show that enterprise′s profits changes steadyly under the stable state and changes valatily, under the chaotic state. When the adjusting speed of input of the enterprise is too large, its average profit falls and the opponents′rises.