Open AccessEmergence of synchronization in Kuramoto model with frustration under general network topology
Author(s) -
Tingting Zhu
Publication year - 2022
Publication title -
networks and heterogeneous media
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.732
H-Index - 34
eISSN - 1556-181X
pISSN - 1556-1801
DOI - 10.3934/nhm.2022005
Subject(s) - digraph , frustration , mathematics , synchronization (alternating current) , topology (electrical circuits) , dissipation , invariant (physics) , kuramoto model , pure mathematics , combinatorics , physics , mathematical physics , thermodynamics , condensed matter physics
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 are confined in half circle. As lack of uniform coercivity in general digraph, we apply the node decomposition criteria in [ 25 ] to capture a clear hierarchical structure, which successfully yields the dissipation mechanism of phase diameter and an invariant set confined in quarter circle after some finite time. Then the dissipation of frequency diameter will be clear, which eventually leads to the synchronization.