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Journal article
Stability of Twisted States in the Kuramoto Model on Cayley and Random Graphs
Journal of nonlinear science, v 25(6), pp 1169-1208
01 Dec 2015
Abstract
The Kuramoto model of coupled phase oscillators on complete, Paley, and ErdAs-R,nyi (ER) graphs is analyzed in this work. As quasirandom graphs, the complete, Paley, and ER graphs share many structural properties. For instance, they exhibit the same asymptotics of the edge distributions, homomorphism densities, graph spectra, and have constant graph limits. Nonetheless, we show that the asymptotic behavior of solutions in the Kuramoto model on these graphs can be qualitatively different. Specifically, we identify twisted states, steady-state solutions of the Kuramoto model on complete and Paley graphs, which are stable for one family of graphs but not for the other. On the other hand, we show that the solutions of the initial value problems for the Kuramoto model on complete and random graphs remain close on finite time intervals, provided they start from close initial conditions and the graphs are sufficiently large. Therefore, the results of this paper elucidate the relation between the network structure and dynamics in coupled nonlinear dynamical systems. Furthermore, we present new results on synchronization and stability of twisted states for the Kuramoto model on Cayley and random graphs.
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Details
- Title
- Stability of Twisted States in the Kuramoto Model on Cayley and Random Graphs
- Creators
- Georgi S. Medvedev - Drexel UniversityXuezhi Tang - Drexel University
- Publication Details
- Journal of nonlinear science, v 25(6), pp 1169-1208
- Publisher
- Springer Nature
- Number of pages
- 40
- Grant note
- DMS 1109367; DMS 1412066 / NSF; National Science Foundation (NSF) 1412066 / Division Of Mathematical Sciences; National Science Foundation (NSF); NSF - Directorate for Mathematical & Physical Sciences (MPS)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000363718400001
- Scopus ID
- 2-s2.0-84945464151
- Other Identifier
- 991019170393604721
InCites Highlights
Data related to this publication, from InCites Benchmarking & Analytics tool:
- Web of Science research areas
- Mathematics, Applied
- Mechanics
- Physics, Mathematical