On the dynamics of traveling phase-oscillators with positive and   negative couplings
  We investigate numerically the dynamics of traveling clusters in systems of phase oscillators, some of which possess positive couplings and others negative couplings. The phase distribution, speed of traveling, and average separation between clusters as well as order parameters for positive and negative oscillators are computed, as the ratio of the two coupling constants and/or the fraction of positive oscillators are varied. The traveling speed depending on these parameters is obtained and observed to fit well with the numerical data of the systems. With the help of this, we describe the conditions for the traveling state to appear in the systems with or without periodic driving. 
J. Choi, M.Y. Choi, B.-G. Yoon
nlin.AO nlin.CD