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Condensed Matter > Disordered Systems and Neural Networks
Title: Synchronization on star-like graphs and emerging $\mathbb{Z}_{p}$ symmetries at strong coupling
(Submitted on 16 Jul 2021 (v1), last revised 16 Mar 2022 (this version, v2))
Abstract: We discuss the aspects of synchronization on inhomogeneous star-like graphs with long rays in Kuramoto model framework. We assume the positive correlation between internal frequencies and degrees for all nodes which supports the abrupt first order synchronization phase transition. It is found that different ingredients of the graph get synchronized at different critical couplings. Combining numerical and analytic tools we evaluate all critical couplings for the long star graph. Surprisingly it is found that at strong coupling there are discrete values of coupling constant which support the synchronized states with emerging $\mathbb{Z}_{p}$ symmetries. The stability of synchronized phase is discussed and the interpretation of phase with emerging $\mathbb{Z}_{p}$ symmetry for the Josephson array on long star graph is mentioned.
Submission history
From: Artem Alexandrov [view email][v1] Fri, 16 Jul 2021 07:49:51 GMT (915kb,D)
[v2] Wed, 16 Mar 2022 10:23:44 GMT (1407kb,D)
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