一类时滞交通流模型的多稳定性研究

Multistability in Delay Car-Following Models

摘要: 众所周知，交通系统是一个十分复杂的非线性大系统，受到诸多因素的制约，建立一个能够准确描述系统特性的数学模型是一项极具挑战性的工作。时滞车辆跟驰模型是指包含司机反映时滞的车辆跟驰模型。本文在已有模型基础上分析了司机反映时滞对车辆跟驰模型复杂动力学行为的影响，如稳定、分岔、多稳定性及混沌等。通过数值模拟与理论分析，揭示了司机反映时滞这一个体特征在驾驶过程中的重要性。

Abstract: It is well-known that traffic system is a complex nonlinear large system. There are a great number of factors to influence the evolutionary behavior of the system. It is a challenging job to propose a mathematical model to accurately describe such a real system. In car following models of traffic dynamics, there exists a finite time for human drivers to process stimuli of preceding vehicles and make a decision. It is natural to give a detailed study of the mechanism about how time delays affect the traffic flow patterns and their evolutions. In this paper, we are interested in rich dynamical behavior in a class of nonlinear car-following models, including stability, Hopf bifurcations, multistability and chaotic behavior etc. Numerical simulation gives a solid verification of our findings.