On the pattern formation mechanism of (2 + 1)D max-plus models

Daisuke Takahashi*, Atsuhiko Shida, Motohiro Usami

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


We propose a max-plus equation which reproduces evolutional patterns often observed in reaction-diffusion systems of excitable media. The equation gives a travelling wave, a target pattern and a spiral pattern from appropriate initial data. Moreover, using the advantages of max-plus equations, we obtain the solutions exactly by a reduction from the high-dimensional equation to a lower one. In the reduction, we use coordinate curves according to a pattern shape. It is interesting that all patterns satisfy the same reduced equation. We also propose two other models similar to the previous one and discuss the behaviour of solutions.

Original languageEnglish
Pages (from-to)10715-10726
Number of pages12
JournalJournal of Physics A: Mathematical and General
Issue number48
Publication statusPublished - 2001 Dec 7

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • General Physics and Astronomy


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