Emergence of synchronization in Kuramoto model with frustration under general network topology

<p style='text-indent:20px;'>In this paper, we will study the emergent behavior of Kuramoto model with frustration on a general digraph containing spanning tree. We provide sufficient condition for emergence asymptotical synchronization if initial data are confined in half circle. As lack uniform coercivity digraph, apply node decomposition criteria [<xref ref-type="bibr" rid="b25">25</xref>] to capture clear hierarchical structure, which successfully yields dissipation mechanism phase diameter and an invariant set quarter circle after some finite time. Then frequency be clear, eventually leads synchronization.</p>