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Chases and Escapes: From Singles to Groups

  • Atsushi Kamimura
  • Shigenori Matsumoto
  • Toru Ohira
Chapter

Abstract

“Chases and escapes” is a traditional mathematical problem. The act of balancing a stick on human fingertips represents an experimental paradigm of typical “one-to-one” chase and escape. Recently, we have proposed a simple model where we extend the chaser and escape to a case a group of particles chasing another group, called “group chase and escape.” This extension connects the traditional problem with current interests on collective motions of animals, insects, vehicles, etc. In this chapter, we present our basic model and its rather complex behavior. In the model, each chaser approaches its nearest escapee, while each escapee steps away from its nearest chaser. Although there are no communications within each group, simulations show segregations of chasers and targets. Two order parameters are introduced to characterize the chasing and escaping in group. Further developments are reviewed to extend our basic model.

Keywords

Chases and escapes Collective motion Traffic model Optimal velocity model Group chase and escape Pattern formation Order parameter 

Notes

Acknowledgements

A.K. is supported by the Japan Society for the Promotion of Science. T.O. has been supported by Kayamori Foundation of Information Science Advancement.

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Copyright information

© Springer Japan 2015

Authors and Affiliations

  • Atsushi Kamimura
    • 1
  • Shigenori Matsumoto
    • 2
  • Toru Ohira
    • 3
  1. 1.Department of Basic ScienceThe University of TokyoKomaba, TokyoJapan
  2. 2.Department of Applied PhysicsThe University of TokyoHongo, TokyoJapan
  3. 3.Graduate School of MathematicsNagoya UniversityFurocho, NagoyaJapan

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