Analytical Results for Frequency-Weighted Kuramoto-Oscillator Networks

The Kuramoto model for an ensemble of coupled oscillators provides a paradigmatic example of non-equilibrium transitions between an incoherent and a synchronized state. A frequency-weighted network of Kuramoto oscillators is proposed, where the oscillators are asymmetrically coupled with the weights depending on their own native frequencies. Moreover, the characteristics of the whole network can be described by a single weighting exponent β. To obtain some analytical results, we focus on three special values of the weighting exponent β. Obviously, the network of oscillators in connection with the heterogeneous coupling scheme turns out to exhibit richer dynamics. Our findings indicate that the weighting exponents should be of importance to affect the network's synchronization ability.