ON THE BASIN OF ATTRACTORS FOR THE UNIDIRECTIONALLY COUPLED KURAMOTO MODEL IN A RING

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We present the long-time dynamics of unidirectionally coupled identical Kuramoto oscillators in a ring, when each oscillator is influenced sinusoidally by a single preassigned oscillator. In this situation, for a large system with N >= 5, it is well known that the synchronized states and the splay-state are the only stable equilibria by Gershgorin's theorem and linear stability analysis, whereas for low-dimensional systems with N = 2, 3 the synchronized state is the unique stable equilibrium. We present nontrivial proper subsets of synchronized and splay-state basins with positive Lebesgue measure in N-phase space. For the threshold case N = 4, we show that the splay-state is nonlinearly unstable by explicit construction of perturbations converging toward the synchronized state asymptotically.
Publisher
SIAM PUBLICATIONS
Issue Date
2012-10
Language
English
Article Type
Article
Citation

SIAM JOURNAL ON APPLIED MATHEMATICS, v.72, no.5, pp.1549 - 1574

ISSN
0036-1399
DOI
10.1137/110829416
URI
http://hdl.handle.net/10203/278724
Appears in Collection
MA-Journal Papers(저널논문)
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