一类混合双寡头模型的分岔分析与混沌控制

The Bifurcation Analysis and Chaos Control of a Mixed Duopoly Model

在有限理性的假设下,建立了由公私合营企业和外资企业组成的生产同质产品的动态混合双寡头模型,分析了该系统的均衡点的存在性和稳定性,并推导出均衡点不会通过Neimark-Sacker分岔失去稳定性.利用Matlab数值模拟了系统在选取不同参数时的动力学行为,结果表明:系统会通过flip分岔进入混沌状态,并且在特定的参数条件下会出现多吸引子共存的现象.此外,还发现调整速度的大小会影响系统的稳定状态,当调整速度较大时,系统更容易变得不稳定而进入混沌状态.对于系统的混沌状态,使用延迟反馈方法实施了有效控制.

Under the assumption of bounded rationality,a dynamical mixed duopoly model consisting of a public-private joint firm and a foreign enterprise is established.The existence and stability of equilibrium point of the system are analyzed,and it is concluded that the equilibrium point cannot loss its stability via Neimark-Sacker bifurcation.The dynamical behaviors of the system when selecting different parameters is numerically simulated by Matlab,the results show that the system will enter the chaotic state through the flip bifurcation.And under some certain parameter conditions,the phenomenon of coexistence of multiple attractors can be found.In addition,it is also found that the speed of adjustment affects the steady state of the built model.When the speed of adjustment is selected large enough,the system is more likely to become unstable and enter a chaotic state.The chaotic state of the system is controlled successfully using the so-called delay feedback method.