Periodic orbit analysis for the deterministic path-preference traffic flow cellular automaton

  • Yoichi NakataEmail author
  • Yoshihiro Ohta
  • Sigeo Ihara
Original Paper Area 1


The path-preference traffic flow cellular automaton is suggested to model the dynamics of transcription. The main difference from the simple traffic flow model is that it contains another preferential paths at some sites. In this paper, we propose an exact analysis for the simplest version of this model. We find that the density of particles is dominant to the dynamics of this cellular automaton and observed that there are not only expected phase shift but also several gaps as the density increases. By considering the behavior of periodic orbits, we also determine the point where such gaps in the flow appear and the exact value of the flow.


Cellular automaton Traffic jams Exact analysis Phase shift Periodic orbit 

Mathematics Subject Classification

90B20 37B15 



We would like to thank Professors Tetsuji Tokihiro and Youichiro Wada for helpful comments. This research is supported by Platform for Dynamic Approaches to Living System (the Platform Project for Supporting in Drug Discovery and Life Science Research) from the Ministry of Education, Culture, Sports, Science (MEXT) and Technology, Japan, and Japan Agency for Medical Research and Development (AMED). This work is also partially supported by the JPSJ KAKENHI Grant Number 17K14199.


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Copyright information

© The JJIAM Publishing Committee and Springer Japan KK, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Isotope Science CenterThe University of TokyoTokyoJapan
  2. 2.Institute of Biology and Mathematics (iBMath), Interdisciplinary Center of Mathematical Sciences, Graduate School of Mathematical SciencesThe University of TokyoTokyoJapan
  3. 3.Research Center for Advanced Science and TechnologyThe University of TokyoTokyoJapan

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