Abstract
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 language | English |
|---|---|
| Pages (from-to) | 10715-10726 |
| Number of pages | 12 |
| Journal | Journal of Physics A: Mathematical and General |
| Volume | 34 |
| Issue number | 48 |
| DOIs | |
| Publication status | Published - 2001 Dec 7 |
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ASJC Scopus subject areas
- Mathematical Physics
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
Cite this
On the pattern formation mechanism of (2 + 1)D max-plus models. / Takahashi, Daisuke; Shida, Atsuhiko; Usami, Motohiro.
In: Journal of Physics A: Mathematical and General, Vol. 34, No. 48, 07.12.2001, p. 10715-10726.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - On the pattern formation mechanism of (2 + 1)D max-plus models
AU - Takahashi, Daisuke
AU - Shida, Atsuhiko
AU - Usami, Motohiro
PY - 2001/12/7
Y1 - 2001/12/7
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0035824416&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0035824416&partnerID=8YFLogxK
U2 - 10.1088/0305-4470/34/48/333
DO - 10.1088/0305-4470/34/48/333
M3 - Article
AN - SCOPUS:0035824416
VL - 34
SP - 10715
EP - 10726
JO - Journal of Physics A: Mathematical and Theoretical
JF - Journal of Physics A: Mathematical and Theoretical
SN - 1751-8113
IS - 48
ER -