Prog. Theor. Phys. Vol. 72 No. 5 (1984) pp. 885-894

[ Full Text PDF : FREE ACCESS (543K) ]

Stability Theory of Synchronized Motion in Coupled-Oscillator Systems. III

— Mapping Model for Continuous System —

Department of Physics, Kyushu Institute of Technology, Kitakyushu 804
^*Department of Physics, Kagoshima University, Kagoshima 890

(Received May 12, 1984)

Abstract:

By starting with a reaction-diffusion equation a mapping model for the continuous system is proposed. The transition from the uniform state to the non-uniform one occurs at the same vaalue of the diffusion constant for the mapping model as for the original reaction-diffusion equation if the transition exists. The mapping model is further studied by adopting the logistic model in one-dimensional space with a peridodic boundary condition. Equal time spectra in wave number space and power spectra for several values of wave numbers are numerically obtained. A comparison of the numerical results of the equal time spectra with a simple theory is made to give a satisfactory agreement for large wave numbers.

URL : http://ptp.ipap.jp/link?PTP/72/885/
DOI : 10.1143/PTP.72.885

References:

R. M. May and G. F. Oster, The American Naturalist 110 (1976), 573.
J. -P. Eckmann, Rev. Mod. Phys. 53 (1981), 643[APS].
H. L. Swinney, Physica 7D (1983), 3[Elsevier].
G. Rowlands, J. of Phys. A16 (1983), 3.
A. H. Fowler and M. J. McGuinness, Physica 5D (1982), 149[Elsevier].
D.Broomhead et al., Phys. Lett. 84A (1981), 229.
T. Yamada and H. Fujisaka, Prog. Theor. Phys. 70 (1983), 1240[PTP].
K. Kaneko, Prog. Theor. Phys. 69 (1983), 1427[PTP].
J. M. Yuan et al., Phys. Rev. A28 (1983), 1662[APS].
Y. Gu et al., Phys. Rev. Lett. A28 (1984), 701[APS].
R. J. Deissler, Phys. Lett. 100A (1984), 451.
K. Kaneko, Prog. Theor. Phys. 72 (1984), 480[PTP].
Y. Kuramoto and T. Yamada, Prog. Theor. Phys. 56 (1976), 679[PTP].
K. Nazaki and N. Bekki, Phys. Rev. Lett. 51 (1983), 2171[APS].
H. Fujisaka and T. Yamada, Prog. Theor. Phys. 69 (1983), 32[PTP].
P. Manneville and Y. Pomeau, Physica 1D (1980), 219[Elsevier].
U. Frisch and R. Morf, Phys. Rev. A23 (1981), 2673[APS].
D. C. Leslie, Rep. Prog. Phys. 36 (1973), 1365[CrossRef].
S. Takesue and K. Kaneko, Prog. Theor. Phys. 71 (1984), 35[PTP].
For example, see J. D. Farmer, Physica 4D (1982), 366[Elsevier].

Citing Article(s) :

Journal of the Physical Society of Japan 67 (1998) pp. 3055-3060 :
Synchronized Chaos in Heterogeneous Systems [rf:99]

Daisuke Katsuragi
Progress of Theoretical Physics Vol. 74 No. 4 (1985) pp. 918-921 :
A New Intermittency in Coupled Dynamical Systems

Hirokazu Fujisaka and Tomoji Yamada
Progress of Theoretical Physics Vol. 74 No. 5 (1985) pp. 1033-1044 :
Spatiotemporal Intermittency in Coupled Map Lattices

Kunihiko Kaneko
Progress of Theoretical Physics Vol. 75 No. 5 (1986) pp. 1087-1104 :
Stability Theory of Synchronized Motion in Coupled-Oscillator Systems. IV

Hirokazu Fujisaka and Tomoji Yamada
Progress of Theoretical Physics Vol. 79 No. 4 (1988) pp. 758-764 :
Characterization of Statistically Homogeneous Fluctuations

Hirokazu Fujisaka and Masayoshi Inoue
Progress of Theoretical Physics Vol. 87 No. 1 (1992) pp. 103-110 :
Synchronized States in Asymmetric Coupled Map Systems

Masayoshi Inoue, Hirokazu Anai, Hiroki Hata and Hirokazu Fujisaka
Progress of Theoretical Physics Vol. 94 No. 4 (1995) pp. 515-534 :
Nearly Synchronized State and a Constant of Motion in a Coupled Chaotic Map

Masayoshi Inoue and Yutaka Nishi
Progress of Theoretical Physics Vol. 95 No. 1 (1996) pp. 45-50 :
Structural Criticality of Dynamical Glass State in a Spatially Coupled Map

Hiroki Hata, Seigo Oku and Kimitoshi Yabe
Progress of Theoretical Physics Vol. 97 No. 3 (1997) pp. 387-398 :
Appearance of an Invariant Manifold and On-Off Intermittency in Coupled-Maps

Masayoshi Inoue, Takashi Kawazoe and Hiroki Hata
Progress of Theoretical Physics Supplement No.99 (1989) pp. 263-287 :
Towards Thermodynamics of Spatiotemporal Chaos

Kunihiko Kaneko