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Information Exchange between Moving Particles and Defects

  • Takashi Teramoto
  • Kei-Ichi Ueda
  • Xiaohui Yuan
  • Yasumasa Nishiura
Conference paper
  • 355 Downloads
Part of the Proceedings in Information and Communications Technology book series (PICT, volume 1)

Abstract

Pulse wave is one of the main careers of information and the effect of heterogeneity of the media in which it propagates is of great importance for the understanding of signaling processes in biological and chemical systems. A typical one dimensional heterogeneity is a spatially localized bump or dent, which creates associated defects in the media. To know the behaviors of pulse in such media is equivalent to study the collision process between the pulse and the defect. A variety of outputs are observed depending on the height and width of the bump such as rebound, pinning, oscillatory motion as well as penetration. A remarkable thing is that PDE dynamics can be reduced to finite dimensional one near a drift bifurcation and the defects become equilibrium points of the reduced ODEs. The basin of each equilibrium point and the switching among those basins explain all the outputs after collision with the defects. We employ a three-component reaction-diffusion system of one-activator-two-inhibitor type to illustrate these issues.

Keywords

Reaction-diffusion system heterogeneous media bifurcation analysis 

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Copyright information

© Springer Tokyo 2009

Authors and Affiliations

  • Takashi Teramoto
    • 1
  • Kei-Ichi Ueda
    • 2
  • Xiaohui Yuan
    • 3
  • Yasumasa Nishiura
    • 3
  1. 1.Chitose Institute of Science and TechnologyChitose 
  2. 2.Research Institute for Mathematical SciencesKyoto UniversityKyoto 
  3. 3.Research Institute for Electronic ScienceHokkaido UniversitySapporo 

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