2007 Fiscal Year Final Research Report Summary
Global Bifurcation Analysis for tindorstruiding and Control of Pattern Dynan-dm
| Project/Area Number |
17540113
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Osaka University |
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Principal Investigator |
OGAWA Toshiyuki Osaka University, Gaduate school of Engineering Science, Associate Professor (80211811)
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| Co-Investigator(Kenkyū-buntansha) |
NAWA Hayato Osaka University, Gaduate school of EngineetingScience, Professor (90218066)
NAKANISHI Shyuji Osaka University, Gaduate school of Engineering Science, Associate Professor (40333447)
KUWAMURA Masataka Kobe University, Gaduate school of Human Development and Enviromnent, Associate Professor (30270333)
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| Project Period (FY) |
2005 – 2007
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| Keywords | Wave Bifurcation / Degenerate Hoof Bifurcation / Bifurcation Analysis / Electro-Chemical Oscillation / 3-component Reaction-Diffusion system / Turing Bifuracation / Pattern Selection |
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| Research Abstract |
Oscillatory Reaction-Diffusion systems are studied from the point of bifurcation analysis to understand the various types of spatio-temporal patterns observed in a certain electro-chemical oscillation. It turned out, first, that a nontrivial oscillatory mode becomes observable by virtue of a global negative inhibition. Second, we see that the mode interactions between ±1 modes determine the pattern selection of rotating and standing waves. Moreover, by this bifurcation analysis we can easily control the result of experiments. We also find that this model can be considered as a special case of 3-component reaction-diffusion system which also exhibits so-called wave bifurcation. Mode interaction between Turing and Wave bifurcation is also studied.
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