An approach to normal forms of Kuramoto model with distributed delays and the effect of minimal delay

摘要: Abstract Heterogeneous delays with positive lower bound (gap) are taken into consideration in Kuramoto model. On the Ott–Antonsen's manifold, dynamical transitional behavior from incoherence to coherence is mediated by Hopf bifurcation. We establish a perturbation technique on complex domain, which universal normal forms, stability and criticality of bifurcation obtained. Theoretically, hysteresis loop found near subcritically bifurcated coherent state. With respect Gamma distributed delay fixed mean variance, we find that large gap decreases value, induces supercritical bifurcations, avoids significantly increases number coexisting states. The effect finally interpreted viewpoint excess kurtosis distribution.