Nonlinear Dynamics

, Volume 76, Issue 1, pp 441–445 | Cite as

TDGL equation in lattice hydrodynamic model considering driver’s physical delay

  • Hong-Xia Ge
  • Peng-Jun Zheng
  • Siu-Ming Lo
  • Rong-Jun Cheng
Original Paper


Based on an extended lattice hydrodynamic model considering the delay of the driver’s response in sensing headway, we get the time-dependent Ginzburg–Landau (for short, TDGL) equation to describe the transition and critical phenomenon in traffic flow by applying the reductive perturbation method. The corresponding solutions are obtained. Numerical simulation is carried out to examine the performance of the model and the results show coincidence with the analysis results.


Traffic flow Lattice hydrodynamic model Time-dependent Ginzburg–Landau equation 



The project has been 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

  • Hong-Xia Ge
    • 1
  • Peng-Jun Zheng
    • 1
  • Siu-Ming Lo
    • 2
  • Rong-Jun Cheng
    • 3
  1. 1.Faculty of Maritime and TransportationNingbo UniversityNingboChina
  2. 2.Department of Civil and Architectural EngineeringCity University of Hong KongKowloonChina
  3. 3.Department of Fundamental Course, Ningbo Institute of TechnologyZhejiang UniversityNingboChina

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