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Prog. Theor. Phys. Vol. 63 No. 6 (1980) pp. 1885-1903

[ Full Text PDF : FREE ACCESS (1176K) ]

Instability and Turbulence of Wavefronts in Reaction-Diffusion Systems

Yoshiki Kuramoto

Department of Physics, Kyoto University, Kyoto 606

(Received September 19, 1979)

Abstract:

The theoretical possibility of a new kind of diffusion-induced chemical turbulence is discussed. Here the nearly planar wavefront of a pulse or phase-boundary propagating through a more than one-dimensional medium is of our concern. By means of an asymptotic method an equation describing the behavior of a curved wavefront is first derived assuming that its spatial variation is slow. The method employed and the resulting equation are completely analogous to those encountered in the theory of turbulent phase waves presented earlier, although the physical situations considered are different. It turns out that if a spontaneous deformation of a planar wavefront occurs, this is immediately accompanied by turbulence provided that the system is well extended. The condition for this kind of instability is shown analytically to be fulfilled by a simple activator-inhibitor model.


URL : http://ptp.ipap.jp/link?PTP/63/1885/
DOI : 10.1143/PTP.63.1885

[ Full Text PDF : FREE ACCESS (1176K) ] Citation:

References:

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Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 68 No. 1 (1982) pp. 129-147 :
    Kinetic Drumhead Models of Interface. II
    Kyozi Kawasaki and Takao Ohta
  2. Progress of Theoretical Physics Vol. 71 No. 6 (1984) pp. 1182-1196 :
    Phase Dynamics of Weakly Unstable Periodic Structures
    Yoshiki Kuramoto
  3. Progress of Theoretical Physics Vol. 73 No. 6 (1985) pp. 1377-1389 :
    Euclidean Invariant Formulation of Phase Dynamics. I
    Takao Ohta
  4. Progress of Theoretical Physics Vol. 89 No. 3 (1993) pp. 599-605 :
    Oscillating Interfaces in Parametrically Forced Systems
    Tsuyoshi Mizuguchi and Shin-ichi Sasa
  5. Progress of Theoretical Physics Supplement No.79 (1984) pp. 223-240 :
    Cooperative Dynamics of Oscillator Community
    Yoshiki Kuramoto
  6. Progress of Theoretical Physics Supplement No.99 (1989) pp. 244-262 :
    On the Reduction of Evolution Equations in Extended Systems
    Yoshiki Kuramoto

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