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Prog. Theor. Phys. Supplement No.64 (1978) pp. 346-367

[ Full Text PDF : FREE ACCESS (1336K) ]

Diffusion-Induced Chaos in Reaction Systems

Yoshiki Kuramoto

Department of Physics, Kyoto University, Kyoto 606

Abstract:

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 toe 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 with 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 discucssed in connection with spatial pattern, so that no discrete approximations, such as a box-model or mode-truncation, are employed.


URL : http://ptp.ipap.jp/link?PTPS/64/346/
DOI : 10.1143/PTPS.64.346

[ Full Text PDF : FREE ACCESS (1336K) ] Citation:

References:

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Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 63 No. 6 (1980) pp. 1885-1903 :
    Instability and Turbulence of Wavefronts in Reaction-Diffusion Systems
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  2. Progress of Theoretical Physics Vol. 63 No. 6 (1980) pp. 2112-2114 :
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    G. I. Sivashinsky and D. M. Michelson
  3. Progress of Theoretical Physics Vol. 66 No. 3 (1981) pp. 1081-1085 :
    Turbulized Rotating Chemical Waves
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  4. Progress of Theoretical Physics Vol. 68 No. 3 (1982) pp. 731-743 :
    Solutions to Non-Linear Reaction-Diffusion Equations in Two Space Dimensions
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  5. Progress of Theoretical Physics Vol. 68 No. 4 (1982) pp. 1105-1121 :
    Multiperiodic Flows, Chaos and Lyapunov Exponents
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  6. Progress of Theoretical Physics Vol. 69 No. 1 (1983) pp. 32-47 :
    Stability Theory of Synchronized Motion in Coupled-Oscillator Systems
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  7. Progress of Theoretical Physics Vol. 71 No. 6 (1984) pp. 1182-1196 :
    Phase Dynamics of Weakly Unstable Periodic Structures
    Yoshiki Kuramoto
  8. Progress of Theoretical Physics Vol. 73 No. 6 (1985) pp. 1377-1389 :
    Euclidean Invariant Formulation of Phase Dynamics. I
    Takao Ohta
  9. Progress of Theoretical Physics Vol. 83 No. 2 (1990) pp. 169-174 :
    Phase Turbulence and Mutual Entrainment in a Coupled Oscillator System
    Hidetsugu Sakaguchi
  10. Progress of Theoretical Physics Vol. 84 No. 5 (1990) pp. 792-800 :
    Breakdown of the Phase Dynamics
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  11. Progress of Theoretical Physics Vol. 88 No. 3 (1992) pp. 593-598 :
    Pattern Formation in Coupled Phase Equations
    Hidetsugu Sakaguchi
  12. Progress of Theoretical Physics Vol. 89 No. 6 (1993) pp. 1123-1146 :
    Phase Dynamics and Localized Solutions to the Ginzburg-Landau Type Amplitude Equations
    Hidetsugu Sakaguchi
  13. Progress of Theoretical Physics Vol. 106 No. 2 (2001) pp. 315-322 :
    Possibility of Soft-Mode Turbulence in Reaction-Diffusion Systems
    Hirokazu Fujisaka and Tomoji Yamada
  14. Progress of Theoretical Physics Supplement No.79 (1984) pp. 223-240 :
    Cooperative Dynamics of Oscillator Community
    Yoshiki Kuramoto
  15. Progress of Theoretical Physics Supplement No.99 (1989) pp. 244-262 :
    On the Reduction of Evolution Equations in Extended Systems
    Yoshiki Kuramoto
  16. Progress of Theoretical Physics Supplement No.99 (1989) pp. 450-457 :
    A New Scheme of Spatio-Temporal Chaos Created by the Interaction between the Phase Waves and the Topoligical Defects
    Satoru Nasuno and Yasuji Sawada

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