Zhang Xiaoyan, Jarrett David F.
Department of Civil and Transportation Engineering, Napier University, Edinburgh EH10 5DT, United Kingdom.
Chaos. 1998 Jun;8(2):503-513. doi: 10.1063/1.166331.
In this paper we investigate the dynamic behavior of road traffic flows in an area represented by an origin-destination (O-D) network. Probably the most widely used model for estimating the distribution of O-D flows is the gravity model, [J. de D. Ortuzar and L. G. Willumsen, Modelling Transport (Wiley, New York, 1990)] which originated from an analogy with Newton's gravitational law. The conventional gravity model, however, is static. The investigation in this paper is based on a dynamic version of the gravity model proposed by Dendrinos and Sonis by modifying the conventional gravity model [D. S. Dendrinos and M. Sonis, Chaos and Social-Spatial Dynamics (Springer-Verlag, Berlin, 1990)]. The dynamic model describes the variations of O-D flows over discrete-time periods, such as each day, each week, and so on. It is shown that when the dimension of the system is one or two, the O-D flow pattern either approaches an equilibrium or oscillates. When the dimension is higher, the behavior found in the model includes equilibria, oscillations, periodic doubling, and chaos. Chaotic attractors are characterized by (positive) Liapunov exponents and fractal dimensions.(c) 1998 American Institute of Physics.
在本文中，我们研究了由起讫点（O-D）网络表示的区域内道路交通流的动态行为。用于估计O-D流分布的最广泛使用的模型可能是重力模型，[J. de D. Ortuzar和L. G. Willumsen，《运输建模》（Wiley，纽约，1990年）]，它起源于与牛顿引力定律的类比。然而，传统的重力模型是静态的。本文的研究基于Dendrinos和Sonis通过修改传统重力模型提出的重力模型的动态版本[D. S. Dendrinos和M. Sonis，《混沌与社会空间动力学》（施普林格出版社，柏林，1990年）]。动态模型描述了O-D流在离散时间段内的变化，例如每天、每周等等。结果表明，当系统维度为一或二时，O-D流模式要么趋向于平衡，要么振荡。当维度更高时，模型中发现的行为包括平衡、振荡、倍周期分岔和混沌。混沌吸引子的特征是（正的）李雅普诺夫指数和分形维数。（c）1998美国物理研究所。
