Traveling Speed of Clusters in the Kuramoto-Sakaguchi Model

다국어 초록 (Multilingual Abstract)

We study a variant of the Kuramoto-Sakaguchi model in which oscillators are divided into twogroups, each characterized by its coupling constant and phase lag. Specifically, we consider the casethat one coupling constant is positive and the other negative, and calculate numerically the travelingspeed of two clusters emerging in the system and the average separation between them, as well asthe order parameters for positive and negative oscillators, as the two coupling constants, phase lags,and the fraction of positive oscillators are varied. An expression explaining the dependence of thetraveling speed on these parameters is obtained and is observed to fit the numerical data well. Withthe help of this, we describe the conditions for the traveling state to appear in the system.

참고문헌 (Reference)

1 Y. Kuramoto, 1975

2 O. Burylko, IEEE 2012

3 Y. Kuramoto, 49 : 569-, 1987

4 J. A. Acebron, 77 : 137-, 2005

5 See, 54 : R2193-, 1996

6 M. K. S. Young, 82 : 648-, 1999

7 S. C. Young, 65 : 041906-, 2002

8 H. Sakaguchi, 76 : 576-, 1986

9 H. Sakaguchi, 79 : 39-, 1988

10 See, 95 : 014101-, 2005

11 H. Hong, 106 : 054102-, 2011

12 H. Hong, 84 : 046202-, 2011

13 H. Hong, 85 : 056210-, 2012

14 Y. M. Lai, 88 : 012905-, 2013

15 P. Ju, 90 : 012903-, 2014

16 최정재, "On the Dynamics of Traveling Phase-oscillators with Positive and Negative Couplings" 한국물리학회 65 (65): 1738-1742, 2014

17 Y. Kuramoto, "Chemical Oscillations, Waves, and Turbulence" Springer-Verlag 1984