2021/08/09 by Tingting Zhu, Zhu, Tingting
Computer Science · #Cellular Automata and Applications #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation
paper · pdf · doi:10.48550/arxiv.2108.03831
openalex publication_date 2021/08/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we will study the emergent behavior of Kuramoto model with frustration on a general digraph containing a spanning tree. We provide a sufficient condition for the emergence of asymptotical synchronization if the initial data is confined in half circle. As lack of uniform coercivity in general digraph, we apply the node decomposition criteria in \citeH-L-Z20 to capture a clear hierarchical structure, which successfully yields the dissipation mechanism of phase diameter and a small invariant set after finite time. Then the dissipation of frequency diameter will be clear, which eventually leads to the synchronization.