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Heterogeneous delays with positive lower bound (gap) are taken intoconsideration in Kuramoto oscillators. We first establish a perturbationtechnique, by which universal normal forms and detailed dynamical behavior ofthis model can be obtained easily. Theoretically, a hysteresis loop is foundnear the subcritically bifurcated coherent state on the Ott-Antonsen'smanifold. For Gamma distributed delay with fixed variance and mean, we findlarge gap destroys the loop and significantly increases in the number ofcoexisted coherent attractors. This result is also explained in the viewpointof excess kurtosis.

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