Jian Gao (BI, RUG)
Synchronization of coupled second-order oscillators
Several mathematical models are used to understand the synchronization of coupled dynamical units. Among them, coupled Kuramoto oscillators is one of the most popular models. Recently, by adding frequency adaptations (inertias), the second-order oscillators model has been proposed and developed to describe the dynamics of several systems: tropical Asian species of fireflies, Josephson junction arrays, goods markets, dendritic neurons, and power grids.
To study the second-order oscillators, we have generalized the self-consistent method and used it to explain typical features of the second-order oscillators different from Kuramoto ones: discontinuous transitions, hysteresis, and appearance of multiple clusters. Moreover, our method has also been used for second-order oscillators with phase shifts and in complex networks. By comparing the second-order oscillators (with inertia) with Kuramoto ones, we aim to answer the question: what is the effect of inertia on synchronization processes?