Synchronization of the Kuramoto model on the complex networks with bimodal intrinsic frequency distribution

In this work, we study the Kuramoto model on scale-free, random and small-world networks with bimodal intrinsic frequency distributions. We consider two models: in one of them, the coupling constant of the ith oscillator is independent of the number of oscillators with which the oscillator interacts, and in the other one the coupling constant is renormalized with the number of oscillators with which the oscillator interacts. For the first model, the time which is required for reaching the stationary state is more than the time which is needed in the second one. Also, for both models the order parameter of the random and scale-free network decreases by increasing the intrinsic frequency with a bimodal distribution. Unlike scale-free and random networks, the order parameter of the small-world network increases by increasing the frequency at first. But later, it decreases and then starts to oscillate.