8-Figured Hysteresis Loop of OV Model

  • T. Nishi
  • D. Takahashi
Conference paper


In this paper, we studied about an extended version of optimal velocity (OV) model, which was originally proposed by Bando et al. [1] We used a ‘2-step function’an OV function and obtained an 8-figured hysteresis loop in phase space. We also succeeded in obtaining the similar hysteresis loop using a smoother OV function.


Phase Space Hysteresis Loop Traffic Flow Granular Flow Steady Solution 
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  1. 1.
    M. Bando, K. Hasebe, A. Nakayama, A. Shibata, and Y. Sugiyama, Phys. Rev. E 51, 1035–1042 (1995).CrossRefGoogle Scholar
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    Y. Sugiyama, Comp. Phys. Comm. 121–122, 399–401 (1999).Google Scholar
  3. 3.
    Y. Sugiyama and H. Yamada, Proceeding of International Workshop of Tra f fic and Granular Flow ‘87, pp. 301–318 ( Springer, Singapore, 1998 ).Google Scholar
  4. 4.
    Y. Sugiyama and H. Yamada, Phys. Rev. E 55, 7749–7752 (1997).CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • T. Nishi
    • 1
  • D. Takahashi
    • 1
  1. 1.Department of Mathematical SciencesWaseda UniversityTokyoJapan

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