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 critical point for phase transition K_c vs. parameters in heterogeneous case. The natural frequency obeys (a), (b) g(ω)=γπ[(ω−Δ)2+γ2] ; (c) g(ω)=γπ[p(ω−Δ)2+γ2+1−p(ω+Δ)2+γ2] , where p represents the height of peak at Δ, with 0 < p < 0.5; (d) g(ω) = 1/2, where ω ∈ (ε −1, ε + 1) and ε > 0 is a bias of uniform distribution.