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Prog. Theor. Phys. Vol. 75 No. 6 (1986) pp. 1319-1327

Cooperative Phenomena in Two-Dimensional 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 20, 1986)

Abstract:

Phase transitions of active rotator systems with short-range coupling are discussed. The constituents of the system which we call active rotators are represented by a phase model of a limit-cycle oscillator or an excitable element, i.e., dφ/dt=ω-bsin φ, (|ω/b|>1 or <1). The rotators are subject to noises, and ferromagnetic type coupling is assumed between them. The effect of infinitesimal noises on a perfectly ordered motion is examined for various spatial dimensions by using a linear approximation. As a result, a macroscopic in-phase oscillation throughout the system turned out impossible for 1 and 2 dimensions, but possible for 3 dimensions. An interesting feature expected for a two-dimensional system is that there is a finite parameter region where characteristic length scale is absent. In order to see the latter feature in more detail, we performed a Langevin simulation for a two-dimensional system, and confirmed the existence of a Kosterlitz-Thouless type parameter region.

URL : http://ptp.ipap.jp/link?PTP/75/1319/
DOI : 10.1143/PTP.75.1319

[ Full Text PDF : FREE ACCESS (429K) ] Citation: Plain Text BiBTeX EndNote(RIS) RSS

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Citing Article(s) :

1. 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

2. Progress of Theoretical Physics Vol. 77 No. 3 (1987) pp. 622-634 :

   Population Dynamics of Randomly Interacting Self-Oscillators. I

   Hiroaki Daido

3. 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

4. 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

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