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Nonlinear Dynamics

, Volume 76, Issue 1, pp 725–731 | Cite as

The theoretical analysis of the anticipation lattice models for traffic flow

  • Rong-Jun Cheng
  • Zhi-Peng Li
  • Peng-Jun Zheng
  • Hong-Xia Ge
Original Paper

Abstract

Based on the anticipation lattice hydrodynamic models, which are described by the partial differential equations, the continuum version of the model is investigated through a reductive perturbation method. The linear stability theory is used to discuss the stability of the continuum model. The Korteweg–de Vries (for short, KdV) equation near the neutral stability line and the modified Korteweg–de Vries (for short, mKdV) equation near the critical point are obtained by using the nonlinear analysis method. And the corresponding solutions for the traffic density waves are derived, respectively. The results display that the anticipation factor has an important influence on traffic flow. From the simulation, it is shown that the traffic jam is suppressed efficiently with taking into account the anticipation effect, and the analytical result is consonant with the simulation one.

Keywords

Traffic flow Lattice hydrodynamic model KdV equation mKdV equation 

Notes

Acknowledgement

Project supported by the National Natural Science Foundation of China (Grant Nos. 11072117, 11372166 and 61074142), the Scientific Research Fund of Zhejiang Provincial, China (Grant No. LY13A010005), Disciplinary Project of Ningbo, China (Grant No. SZXL1067) and the K.C. Wong Magna Fund in Ningbo University, China.

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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Rong-Jun Cheng
    • 1
  • Zhi-Peng Li
    • 2
  • Peng-Jun Zheng
    • 3
  • Hong-Xia Ge
    • 3
  1. 1.Department of Fundamental Course, Ningbo Institute of TechnologyZhejiang UniversityNingboChina
  2. 2.College of Electronics and Information EngineeringTongji UniversityShanghaiChina
  3. 3.Faculty of Maritime and TransportationNingbo UniversityNingboChina

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