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Prog. Theor. Phys. Vol. 75 No. 5 (1986) pp. 1105-1110

[ Full Text PDF : FREE ACCESS (324K) ]

Phase Transitions in Active Rotator Systems

Shigeru Shinomoto and Yoshiki Kuramoto*

Research Institute for Fundamental Physics, Kyoto University, Kyoto 606
*Department of Physics, Kyoto University, Kyoto 606

(Received February 5, 1986)

Abstract:

In order to study the statistical dynamics of a large population of limit cycle oscillators or excitable elements, an active rotator model is introduced. This is defined dynamically as a stochastic version of a relaxational plannar model (with external field or anisotropy) modified by an additional constant driving force. Its numerical study based on a mean field treatment revealed the existence of a peculiar ordered phase in which individual motions are organized into a macroscopic rhythm. Two possible types of Transition to this ordered phase are also found.


URL : http://ptp.ipap.jp/link?PTP/75/1105/
DOI : 10.1143/PTP.75.1105

[ Full Text PDF : FREE ACCESS (324K) ] Citation:

References:

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Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 75 No. 6 (1986) pp. 1319-1327 :
    Cooperative Phenomena in Two-Dimensional Active Rotator Systems
    Shigeru Shinomoto and Yoshiki Kuramoto
  2. Progress of Theoretical Physics Vol. 76 No. 3 (1986) pp. 576-581 :
    A Soluble Active Rotater Model Showing Phase Transitions via Mutual Entertainment
    Hidetsugu Sakaguchi and Yoshiki Kuramoto
  3. Progress of Theoretical Physics Vol. 77 No. 3 (1987) pp. 622-634 :
    Population Dynamics of Randomly Interacting Self-Oscillators. I
    Hiroaki Daido
  4. Progress of Theoretical Physics Vol. 79 No. 1 (1988) pp. 39-46 :
    Cooperative Phenomena in Coupled Oscillator Systems under External Fields
    Hidetsugu Sakaguchi
  5. Progress of Theoretical Physics Vol. 79 No. 3 (1988) pp. 600-607 :
    Phase Transitions and Their Bifurcation Analysis in a Large Population of Active Rotators with Mean-Field Coupling
    Hidetsugu Sakaguchi, Shigeru Shinomoto and Yoshiki Kuramoto
  6. 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
  7. 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
  8. Progress of Theoretical Physics Vol. 86 No. 6 (1991) pp. 1159-1176 :
    Mutual Entrainment between Populations of Coupled Oscillators
    Koji Okuda and Yoshiki Kuramoto
  9. Progress of Theoretical Physics Supplement No.150 (2003) pp. 48-56 :
    On the Second Variation of Free Energies and Nonlinear Fokker-Planck Equations Involving Periodic Variables
    Till D. Frank

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