Relaxation dynamics of Kuramoto model with heterogeneous coupling<xref rid="cpb_28_12_120503fn1" ref-type="fn">*</xref><fn id="cpb_28_12_120503fn1"><label>*</label><p>Project supported by the National Natural Science Foundation of China (Grant Nos. 11905068, 11847013, 11175150, and 11605055), Postgraduate Research and Practice Innovation Project for Graduate Students of JiangSu Province, China (Grant No. KYCX18-2100), and the Scientific Research Funds of Huaqiao University, China (Grant No. 605-50Y17064).</p></fn>

Relaxation dynamics of Kuramoto model with heterogeneous coupling**

Project supported by the National Natural Science Foundation of China (Grant Nos. 11905068, 11847013, 11175150, and 11605055), Postgraduate Research and Practice Innovation Project for Graduate Students of JiangSu Province, China (Grant No. KYCX18-2100), and the Scientific Research Funds of Huaqiao University, China (Grant No. 605-50Y17064).

Pan Tianwen¹, Huang Xia², Xu Can^{3, †}, Lü Huaping^{1, ‡}

The decay of δ D(t) and δ Z(t) in the in-frequency-weighted case with different K (K < K_c). The solid lines are the direct numerical solutions of Eq. (3) (here K_i = 1 and G_j = K ω_j) and the dashed lines are the fitted curves with exponent as Eqs. (36) and (37). The natural frequency obeys g(ω)=γπ[(ω−Δ)2+γ2] . (a) and (b) K = 1.6, Δ = 0.5, γ = 0.5. (c) and (d) K = 1.4, Δ = 0.5, γ = 0.5. In the numerical simulations, we set the total number of oscillators to N = 100000, and the initial phases for all oscillators are identical.