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

摘要

Oscillator networks with an asymmetric bipolar distribution of naturalfrequencies are used to describe stable operations in electrical transmissiongrids. We propose a mean-field model that captures the onset and form offrequency synchronization in such oscillator networks. The model takes intoaccount a broad class of heterogeneous connection structures. It yieldscritical thresholds and a closed-form description of the synchronized state,identifying basic properties that synchronized regimes possess on allconsidered topologies. The framework also captures synchronized regimes withlarge phase differences that commonly appear just above the critical threshold.Additionally, two model quantities gauge the accuracy of mean-fieldassumptions.