2009 Fiscal Year Final Research Report
Mathematical Structure of Soliton and Chaos in Sequential Cellular Automata
| Project/Area Number |
19740053
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Future University-Hakodate (2007, 2009)
Sapporo Medical University (2008) |
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Principal Investigator |
YURA Fumitaka Future University-Hakodate, システム情報科学部, 准教授 (90404805)
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| Project Period (FY) |
2007 – 2009
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| Keywords | 離散数学 / ソリトン系 / 有限体 |
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| Research Abstract |
We have clarified the existence of soliton system on sequential cellular automata (CA) by the reduction to discrete hungry Lotka-Volterra equation and have analyzed the reason why this model can involve such integrable system as this one.
The (filter-type) CAs which consist of finite states are considered. As a result, finite-field-valued soliton systems are obtained. There exist several studies on integrable systems over finite fields in the past, however, it seems probable that soliton systems over finite fields have not been shown as far as we know. This novel system could give seminal development in integrable systems because the algebraic structure of finite fields is different from that of real numbers and max-plus algebra.
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