Diffusion-Induced Chaos in Reaction Systems
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概要
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A turbulent state in a distributed chemical reaction system is studied theoretically. The chaotic behavior here is basically due to the unstable growth of a spatial inhomogeneity taking place in an oscillating medium. It is argued that phase turbulence and amplitude turbulence have to be discriminated from each other according to their distinct origins. Two prototype equations describing respective types of turbulence are derived by means of some asymptotic methods, and their solutions turn out to exhibit successive bifurcations. It is found that the phase turbulence arises essentially from the interaction among a few unstable phase modes, while the amplitude turbulence may well appear in the presence of only one unstable mode which is a mixed mode of the phase and amplitude. In particular, some similarity of the amplitude turbulence to the Lorenz chaos is pointed out. Throughout the present paper, the chaotic behavior is discussed in connection with spatial pattern, so that no discrete approximations, such as a box-model or mode-truncation, are employed.
- 理論物理学刊行会の論文
- 1979-04-01
著者
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Kuramoto Y
Kyoto Univ. Kyoto Jpn
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Kuramoto Yoshiki
Department Of Mathematics Graduate School Of Science Hokkaido University
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KURAMOTO Yoshiki
Department of Physics, Faculty of Science, Kyushu University
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