Max-min-plus expressions for one-dimensional particle cellular automata obtained from a fundamental diagram

@article{Okumura2013MaxminplusEF,
  title={Max-min-plus expressions for one-dimensional particle cellular automata obtained from a fundamental diagram},
  author={Takazumi Okumura and Junta Matsukidaira and Daisuke A. Takahashi},
  journal={Journal of Physics A},
  year={2013},
  volume={46},
  pages={295101}
}
We study one-dimensional neighborhood-five conservative cellular automata (CA), referred to as particle cellular automata five (particle CA5). We show that evolution equations for particle CA5s that belong to certain types can be obtained in the form of max–min-plus expressions from a fundamental diagram. The obtained equations are transformed into other max–min-plus expressions by ultradiscrete Cole–Hopf transformations, which enable us to analyze the asymptotic behaviors of general solutions… 
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