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Analysis in Kantorovich Geometric Space for Quasi-stable Patterns in 2D-OV Model

In: Traffic and Granular Flow '15

Author

Listed:
  • Ryosuke Ishiwata

    (Nagoya University, Department of Complex Systems Science)

  • Yuki Sugiyama

    (Nagoya University, Department of Complex Systems Science)

Abstract

TheIshiwata, Ryosuke two-dimensional optimalSugiyama, Yuki velocity (2D-OV) model, which consists of self-driven particles, reproduces a big variety of dynamical patterns as seen in biological collective motions (Sugiyama (2009) Natural Computing. Springer Japan, Tokyo [7]). We perform simulations of the 2D-OV model in a simple maze. Dynamically stable patterns are observed from the simulation results. The stability of the patterns seems to be related to a kind of degeneracy of a state. In order to look for some physical quantity, which can indicate the relation between the stability and the degeneracy, we construct a geometric space based on the Kantorovich distance among patterns and represent the changing of flow pattern as the trajectory in the geometric space. As a result, a point corresponding to distributions of particles for the quasi-stable pattern converges to the localised region in the space.

Suggested Citation

  • Ryosuke Ishiwata & Yuki Sugiyama, 2016. "Analysis in Kantorovich Geometric Space for Quasi-stable Patterns in 2D-OV Model," Springer Books, in: Victor L. Knoop & Winnie Daamen (ed.), Traffic and Granular Flow '15, pages 427-433, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-33482-0_54
    DOI: 10.1007/978-3-319-33482-0_54
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