Optimal polarity alignment strength for synchronization. Time evolution of (A) the average phase order parameter 〈Z(t)〉 and (B) the mean squared difference of displacement vectors m(t) for the different ratios of the polarity alignment strength to the polarity noise intensity κφ/Dφ. (C) Dependence of the mixing rate λ on κφ/Dφ. (D) Dependence of 〈Z〉 on κφ/Dφ. 〈Z〉 at several time points is plotted. (E) Dependence of 〈Z〉 at t = 100 on κφ/Dφ for different domain lengths L. In all panels, v0 = 1.2, μ = 10, Dφ = 0.5, ω = 2.1, and Dθ = 0.1 in Eqs. 1–5. Error bars in (A, D, and E) indicate the SD. In (A–D), L = 24 and N = 800. In (E), N = 400,800,1600 for L = 17,24,34, respectively. To see this figure in color, go online.