2002 Fiscal Year Final Research Report Summary
Understanding of Spatio-temporal patterns by Singular Limit Methods
| Project/Area Number |
11214201
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| Research Category |
Grant-in-Aid for Scientific Research on Priority Areas (B)
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| Allocation Type | Single-year Grants |
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| Review Section |
Science and Engineering
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| Research Institution | Hokkaido University |
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Principal Investigator |
NISHIURA Yasumasa Hokkaido University, Research Institute for Electronic Science, Professor, 電子科学研究所, 教授 (00131277)
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| Co-Investigator(Kenkyū-buntansha) |
EI Shin-ichiro Yokohama City University, Grad. School of Integrated Sciences, Associate Professor, 大学院・総合理学研究科, 助教授 (30201362)
OHTA Takao Hiroshima University, Grad. School of Science, Professor, 大学院・理学研究科, 教授 (50127990)
KOBAYASHI Ryo Hokkaido University, RIES, Associate Professor, 電子科学研究所, 助教授 (60153657)
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| Project Period (FY) |
1999 – 2001
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| Keywords | Reaction diffusion system / Crystal growth / Transient dynamics / Pulse dynamics / Chaos / Computer-aided-analysis / Dynamical system / Bifurcation |
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| Research Abstract |
The essence of the singular limit method is to extract a skeleton structure from complex dynamics. A typical example is a class of interfacial equations derived from PDEs by using differences of space-time scales. The resulting equations inherit the essential parts of original dynamics. Our project not only extend its validity to a variety of systems but also present a new approach to complex dynamics, for instance self-replicating dynamics and self-destruction process, which have been regarded as transient dynamics, therefore remain as open questions. The highlight of our approach is three-fold : (a) Geometric characterization for the set of global bifurcating branches that drives complex dynamics. (b) Pulse-pulse interaction method which clarifies the onset of complex dynamics as well as weak interaction among localized patterns. (c) Organizing centers of high codimensions which explains an origin of complex dynamics in a miniature size.
Numerical approach with the aid of path-tracking software like AUTO is indispensable to accomplish the above issues, especially (a). These methods works very well in a harmonized way to understand the whole aspects of complex dynamics and has a great potential to be applied to other fields. The main investigator Yasumasa Nishiura was awarded "Autumn Prize" by Japan Mathematical Society in 2002.
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