Mean-field approach for frequency synchronization in complex networks of two oscillator types

Abstract: Oscillator networks with an asymmetric bipolar distribution of natural frequencies are useful representations of power grids. We propose a mean-field model that captures the onset, form and linear stability of frequency synchronization in such oscillator networks. The model takes into account a broad class of heterogeneous connection structures and identifies a functional form as well as basic properties that synchronized regimes possess classwide. The framework also captures synchronized regimes with large phase differences that commonly appear just above the critical threshold. Additionally, the accuracy of mean-field assumptions can be gauged internally through two model quantities. With our framework, the impact of local grid structure on frequency synchronization can be systematically explored.