一类非线性车辆跟驰模型的稳定性与分岔特性

针对一类常用的非线性车辆跟驰模型，本文运用时滞动力系统理论，分析了由3辆车组成的系统的稳定性及其Hopf分岔特性，得到了系统参数平面上的稳定域范围，以及不同的系统时滞量（驾驶员反映时间）和不同的安全间距对系统稳定域的影响，揭示了非线性车辆跟驰模型中存在的复杂动力学现象。通过数值仿真验证了理论分析和计算的结果，并判明了系统经历的Hopf分岔是亚临界的。理论分析的结果可推广到由任意辆车组成的车队。

Analysis of Stability and Bifurcation of a Class of Car-Following Models

By using the theories of time delay dynamical systems, the stability and bifurcation behavior of a class of nonlinear car-following models consisting of three cars were analyzed. The stable regions in the parameter plane were obtained and the influences on the stable regions for the different time delays （drivers＇ reaction time） and safety space were investigated. The complex dynamical phenomena in nonlinear car-following models were revealed. Finally, some numerical simulations were performed to verify the analytical results and showed a subcritical Hopf bifurcation in the systems. The results of this paper can be easily extended to the system consisting of arbitrary number of cars.