The last paper with Jian Gao on the collective dynamics of second-order oscillators has been accepted for publication in Chaos. From the paper:
The synchronization process in oscillator networks, such as in the Kuramoto model, is typically driven by the formation of a large synchronized cluster that gradually absorbs more oscillators. This process can be disrupted by the formation of smaller synchronized clusters that compete with the main one. Such smaller clusters lead to non-stationary states where the order parameter varies periodically in time in contrast to coherent stationary states where it is constant. In this paper, we consider oscillators with inertia and we study the formation of smaller synchronized clusters. We find that inertia plays a crucial role in the formation of such clusters and the increase of inertia leads to a strengthening of the secondary clusters at the expense of the main cluster. We use numerical experiments, a theoretical analysis of the mean-field equations, and a simplified model to explain different aspects of the formation of secondary synchronized clusters and non-stationary states.