1996 Fiscal Year Final Research Report Summary
Experimental Mathematics for Constitution and Computation in Complex Systems
| Project/Area Number |
07309017
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| Research Category |
Grant-in-Aid for Scientific Research (A)
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| Allocation Type | Single-year Grants |
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| Section | 総合 |
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| Research Field |
広領域
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| Research Institution | Hokkaido University |
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Principal Investigator |
TSUDA Ichiro Hokkaido Univ., Graduate School of Science, Prof., 大学院・理学研究科, 教授 (10207384)
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| Co-Investigator(Kenkyū-buntansha) |
KANEKO Kunihiko Tokyo Univ., Graduate School of Coll.Culture, Prof., 大学院・総合文化研究科, 教授 (30177513)
TAKAHASHI Yoichiro Kyoto Univ., Institute for Mathematical Analysis, Prof., 数理解析研究所, 教授 (20033889)
OKABE Yasunori Tokyo Univ., Graduate School of Engineering, Prof., 大学院・工学研究科, 教授 (30028211)
NISHIURA Yasumasa Hokkaido Univ., Electr.Sci.Institute, Prof., 電子科学研究所, 教授 (00131277)
TSUJISHITA Tohru Hokkaido Univ., Graduate School of Science, Prof., 大学院・理学研究科, 教授 (10107063)
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| Project Period (FY) |
1995 – 1996
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| Keywords | Concurrent process / Coupled map lattices / Chaotic Itinerancy / Langevin equations / Variational principle / Category theory / Logic-dynamics transformation / Internal observers / Chaotic dynamical systems |
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| Research Abstract |
Experimental mathematics method for constitution and computation in complex systems were developed. Complex systems are defined as systems which cannot be analyzed by reductionist's method, that is, a method of "divide-and-concur" that ancient Roman emperors adopted, but rather be easily understood via constitution or its process of such systems.
Many researchers from various kinds of research fields gathered together in Sapporo, and discussed intensively and extensively what a central method should be. Several methods were clarified.
1. Coupled map lattices are useful for the purpose of seeking a universality at intermediate levles which is hidden at both microscopic and macroscopic levels.
2. A new type of stochastic theory is necessary for analysing a high dimensional chaos.
3. A geometric and variational method is useful for a mechanism of high-dimensional spatio-temporal patterns.
4. Logics and category theory is a tool for concurrent process of network systems.
5. A transformation between logics and dynamics is effective for a system where a different levels of dynamics interfere.
6. An observer-oriented theory is essential for constructing an adequate language for complex systems.
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