| Project/Area Number |
08640221
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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 |
解析学
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| Research Institution | KUMAMOTO UNIVERSITY |
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Principal Investigator |
NAITO Koichiro Kumamoto Univ., Dept.Eng., Prof., 工学部, 教授 (10164104)
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| Co-Investigator(Kenkyū-buntansha) |
HISHIDA Toshiaki Niigata Univ., Dept.Eng., Lect., 工学部, 講師 (60257243)
YOKOYAMA Takahisa Kumamoto Univ., Dept.Eng., Lect., 工学部, 講師 (20240864)
KADOTA Noriya Kumamoto Univ., Dept.Eng., Lect., 工学部, 講師 (80185884)
SAISHO Yasumasa Kumamoto Univ., Dept.Eng., A-Prof., 工学部, 助教授 (70195973)
OSHIMA Yoichi Kumamoto Univ., Dept.Eng., Prof., 工学部, 教授 (20040404)
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| Project Period (FY) |
1996 – 1997
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| Project Status |
Completed (Fiscal Year 1997)
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| Budget Amount *help |
¥2,200,000 (Direct Cost: ¥2,200,000)
Fiscal Year 1997: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 1996: ¥1,400,000 (Direct Cost: ¥1,400,000)
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| Keywords | nonlinear evolution equation / almost periodicity / attractor / Fractal dimension / Diophantine approximation |
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| Research Abstract |
In recent years great efforts have been made to analyze complexity or chaotic behaviors in the study of population dynamics or reaction-diffusion models. In this research we investigate almost periodic attractors for the semilinear partial differential equations by estimating their fractal dimensions. Especially, in [1] and [2] (of 11.REF.) we study a reaction-diffusion equation, assuming the periodicity of the diffusion coefficient and the nonlinear reaction function, as a model of population dynamics which has seasonal fluctuations in the diffusion rates. By using simultaneous Diophantine approximation, we can show that the dimension of the almost periodic attractor is majorized by the exponents of Holder's conditions on these periodic functions. Furthermire, in [3] we investigate a quasi-periodic solution of a linear Schrodinger equation with a quasi periodic perturbation with respect to the space variables. We can estimate the fractal dimension of the range of the solution, constructing the epsilon-almost periods, the epsilon-synchronous points in other words, by the iterative method, which depends on the simultaneous approximation for the irrational numbers of the frequencies.
Calculating the dimensions of the attractors is to measure their level of complexity and randomness. On the other hand, it is well known that periodic or almost periodic states occupy the important positions as main gateways in various routes to chaos. In the following papers (of 11.REF.) by the head and co-investigators we have shown various fundamental results, which will play important and essential roles for investigating chaotic behaviors of nonlinear dynamical models.
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