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STABILIZATION ANALYSIS AND MODIFIED KdV EQUATION OF LATTICE MODELS WITH CONSIDERATION OF RELATIVE CURRENT

Author

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  • ZHIPENG LI

    (Department of Information and Communication Engineering, Tongji University, Shanghai 200092, China)

  • XINGLI LI

    (Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China)

  • FUQIANG LIU

    (Department of Information and Communication Engineering, Tongji University, Shanghai 200092, China)

Abstract

In this paper, the lattice model which depends not only on the difference of the optimal current and the local current but also on the relative current is presented and analyzed in detail. We derive the stability condition of the extended model by considering a small perturbation around the homogeneous flow solution with finding that the improvement in the stability of the traffic flow is obtained by taking into account the relative current, which is also confirmed by direct simulations. Moreover, from the nonlinear analysis to the extended models, the relative current dependence of the propagating kink solutions for traffic jam is obtained by deriving the modified KdV equation near the critical point by using the reductive perturbation method.

Suggested Citation

  • Zhipeng Li & Xingli Li & Fuqiang Liu, 2008. "STABILIZATION ANALYSIS AND MODIFIED KdV EQUATION OF LATTICE MODELS WITH CONSIDERATION OF RELATIVE CURRENT," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 19(08), pages 1163-1173.
    • Handle: RePEc:wsi:ijmpcx:v:19:y:2008:i:08:n:s0129183108012868
    DOI: 10.1142/S0129183108012868
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    Citations

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    Cited by:

    1. Wang, Yunong & Cheng, Rongjun & Ge, Hongxia, 2017. "A lattice hydrodynamic model based on delayed feedback control considering the effect of flow rate difference," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 479(C), pages 478-484.
    2. Pan, Dong-Bo & Zhang, Geng & Jiang, Shan & Zhang, Yu & Cui, Bo-Yuan, 2021. "Delay-independent traffic flux control for a discrete-time lattice hydrodynamic model with time-delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 563(C).
    3. Liu, Yi & Cheng, Rong-jun & Lei, Li & Ge, Hong-xia, 2016. "The influence of the non-motor vehicles for the car-following model considering traffic jerk," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 463(C), pages 376-382.

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