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Prog. Theor. Phys. Vol. 63 No. 1 (1980) pp. 106-121

[ Full Text PDF : FREE ACCESS (1066K) ]

Localized Patterns in Reaction-Diffusion Systems

Shinji Koga and Yoshiki Kuramoto

Department of Physics, Kyoto University, Kyoto 606

(Received June 26, 1979)

Abstract:

A new chemical pattern is discussed, which is a propagationless solitary island in an infinite medium. We demonstrate analytically its existence and stability for a certain simple model. The localization turns out to be a consequence of the rapid diffusion of an inhibiting substance occurring in a potentially excitable system. In order to extract the important features of the localized pattern, the method of singular perturbation is employed, with the following results: (1) A stable motionless solitary pattern can exist either for a monostable or bistable system. (2) Under suitable conditions such a pattern undergoes the Hopf bifurcation, leading to a “breathing motion” of the activated droplet.
The analysis is restricted to the one-dimensional case throughout.


URL : http://ptp.ipap.jp/link?PTP/63/106/
DOI : 10.1143/PTP.63.106

[ Full Text PDF : FREE ACCESS (1066K) ] Citation:

References:

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Citing Article(s) :

  1. Journal of the Physical Society of Japan 65 (1996) pp. 1967-1970 :
    Collision of Domain Boundaries in a Reaction-Diffusion System
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  2. Journal of the Physical Society of Japan 66 (1997) pp. 598-606 :
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  3. Journal of the Physical Society of Japan 66 (1997) pp. 1551-1558 :
    Collision of Propagating Pulses in a Reaction-Diffusion System
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  4. Journal of the Physical Society of Japan 81 (2012) 024802 (6 pages) :
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  5. Progress of Theoretical Physics Vol. 63 No. 6 (1980) pp. 1885-1903 :
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  6. Progress of Theoretical Physics Vol. 87 No. 4 (1992) pp. 1055-1058 :
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  7. Progress of Theoretical Physics Vol. 90 No. 6 (1993) pp. 1361-1366 :
    Stably Propagating Periodic Waves in Intrinsically Bistable Reaction-Diffusion Systems
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  8. Progress of Theoretical Physics Vol. 104 No. 1 (2000) pp. 55-61 :
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  9. Progress of Theoretical Physics Vol. 119 No. 5 (2008) pp. 725-738 :
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  10. Progress of Theoretical Physics Supplement No.99 (1989) pp. 425-441 :
    Decay of Metastable Rest State in Excitable Reaction-Diffusion System
    Takao Ohta

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