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Prog. Theor. Phys. Vol. 76 No. 3 (1986) pp. 576-581

[ Full Text PDF : FREE ACCESS (278K) ]

A Soluble Active Rotater Model Showing Phase Transitions via Mutual Entertainment

Hidetsugu Sakaguchi and Yoshiki Kuramoto

Department of Physics, Kyoto University, Kyoto 606

(Received April 17, 1986)

Abstract:

Some analytical results are obtained for a large population of limit-cycle oscillators modelled by a set of deterministic equations \dotφ = ωi-N-1K ΣNj=1 sin (φi-φj+α) (i=1,2, …, N), where φi is the phase of the i-th oscillator and ωi's are parameters distributed randomly. The present work is a generalization of the previous one where the study was limited to the case of vanishing α and symmetric distribution of ωi. As in the previous case, a particular macroscopic solution of steady rotation is found, which branches off the trivial solution at some positive K. A computer simulation with N=1000 is carried out, which correctly reproduces our analytical results.


URL : http://ptp.ipap.jp/link?PTP/76/576/
DOI : 10.1143/PTP.76.576

[ Full Text PDF : FREE ACCESS (278K) ] Citation:

References:

  1. A. T. Winfree, J. Theor. Biol. 16 (1967), 15.
  2. Y. Kuramoto, in Lecture Notes in Phys. (Springer-Verlag, 1975), vol. 39, p. 420.
  3. Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence (Springer-Verlag, 1984).
  4. Y. Kuramoto, Prog. Theor. Phys. Suppl. No. 79 (1984), 223[PTP].
  5. Y. Aizawa, Prog. Theor. Phys. 56 (1976), 703[PTP].
  6. A. T. Winfree, The Geometry of Biological Time (Springer-Verlag, 1980).
  7. Y. Kuramoto, Physica 106A (1981), 128.
  8. Y. Yamaguchi, K. Kometani and H. Shimizu, J. Stat. Phys. 26 (1981), 719.
  9. Y. Yamaguchi and H. Shimizu, Physica 11D (1984), 212[Elsevier].
  10. G. B. Ermentrout and N. Kopell, SIAM J. Math. Anal. 15 (1984), 215.
  11. G. B. Ermentrout, J. Math. Biol. 22 (1985), 1.
  12. S. Shinomoto and Y. Kuramoto, Prog. Theor. Phys. 75 (1986), 1105[PTP].
  13. S. Shinomoto and Y. Kuramoto, Prog. Theor. Phys. 75 (1986), 1319[PTP].
  14. H. Daido, Prog. Theor. Phys. 75 (1986), 1460[PTP].

Citing Article(s) :

  1. Journal of the Physical Society of Japan 69 (2000) pp. 3545-3551 :
    Mutual Entrainment and Multi-Stability in Josephson Junction Arrays
    Hidetsugu Sakaguchi and Kazutaka Watanabe
  2. Journal of the Physical Society of Japan 72 (2003) pp. 1334-1337 :
    Dynamically Coupled Oscillators: Cooperative Behavior via Dynamical Interaction
    Toru Aonishi and Masato Okada
  3. Journal of the Physical Society of Japan 79 (2010) 114001 (9 pages) :
    Dynamics of Retrieval Process in Coupled Oscillator Models with Scattered Natural Frequency
    Satoshi Kawaguchi
  4. Journal of the Physical Society of Japan 81 (2012) 074005 (7 pages) :
    Cascade Failure in a Phase Model of Power Grids
    Hidetsugu Sakaguchi and Tatsuma Matsuo
  5. Progress of Theoretical Physics Vol. 77 No. 3 (1987) pp. 622-634 :
    Population Dynamics of Randomly Interacting Self-Oscillators. I
    Hiroaki Daido
  6. Progress of Theoretical Physics Vol. 77 No. 5 (1987) pp. 1005-1010 :
    Local and Grobal Self-Entrainments in Oscillator Lattices
    Hidetsugu Sakaguchi, Shigeru Shinomoto and Yoshiki Kuramoto
  7. Progress of Theoretical Physics Vol. 79 No. 1 (1988) pp. 39-46 :
    Cooperative Phenomena in Coupled Oscillator Systems under External Fields
    Hidetsugu Sakaguchi
  8. Progress of Theoretical Physics Vol. 79 No. 5 (1988) pp. 1069-1079 :
    Mutual Entrainment in Oscillator Lattices with Nonvariational Type Interaction
    Hidetsugu Sakaguchi, Shigeru Shinomoto and Yoshiki Kuramoto
  9. Progress of Theoretical Physics Vol. 81 No. 4 (1989) pp. 727-731 :
    Intrinsic Fluctuation and Its Critical Scaling in a Class of Populations of Oscillators with Distributed Frequencies
    Hiroaki Daido
  10. Progress of Theoretical Physics Vol. 81 No. 5 (1989) pp. 939-945 :
    Mutual Entrainment of Two Limit Cycle Oscillators with Time Delayed Coupling
    H. G. Schuster and P. Wagner
  11. Progress of Theoretical Physics Vol. 88 No. 6 (1992) pp. 1213-1218 :
    Order Function and Macroscopic Mutual Entrainment in Uniformly Coupled Limit-Cycle Oscillators
    Hiroaki Daido
  12. Progress of Theoretical Physics Vol. 89 No. 4 (1993) pp. 929-934 :
    Critical Conditions of Macroscopic Mutual Entrainment in Uniformly Coupled Limit-Cycle Oscillators
    Hiroaki Daido
  13. Progress of Theoretical Physics Vol. 91 No. 4 (1994) pp. 693-698 :
    Desynchronization in a Population of Globally Coupled Identical Oscillators
    Hidetsugu Sakaguchi
  14. Progress of Theoretical Physics Vol. 97 No. 6 (1997) pp. 849-857 :
    Complex Dynamics in a Population of Threshold Elements
    Hidetsugu Sakaguchi
  15. Progress of Theoretical Physics Vol. 104 No. 4 (2000) pp. 709-721 :
    Stability Gap between Off- and On-Firing States in a Coupled Ginzburg-Landau Oscillator Neural Network
    Satoshi Kawaguchi
  16. Progress of Theoretical Physics Vol. 107 No. 5 (2002) pp. 839-860 :
    Oscillation of the Overlap Parameter in a Phase Coupled Model
    Satoshi Kawaguchi
  17. Progress of Theoretical Physics Vol. 110 No. 6 (2003) pp. 1047-1057 :
    Synchronization in Oscillator Systems with a Central Element and Phase Shifts
    Yakov Kazanovich and Roman Borisyuk

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