Emergent behaviors of Kuramoto model with frustration under switching topology

Abstract

In this paper, we study the emergent behavior of Kuramoto model with switching topology under the effect of uniform frustration. In our frameworks, the switching interaction topology contains a spanning tree in any switching mode. For the initial configuration distributed in an open half circle, we first exploit a similar procedure in [T. Zhu, Netw. Heterog. Media, 17(2):255-291, 2022] to conclude that the Kuramoto oscillators will be pushed into a small region at some instant before the first network switching. Then in a large coupling and small frustration regime, we lift the Kuramoto model to the second-order formulation and apply the matrix theory-based approach in [J.-G.