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29 March 2024
 
  » arxiv » cond-mat/0606048

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Synchronization transition of heterogeneously coupled oscillators on scale-free networks
E. Oh ; D.-S. Lee ; B. Kahng ; D. Kim ;
Date 2 Jun 2006
Subject Statistical Mechanics
AbstractWe investigate the synchronization transition of the modified Kuramoto model where the oscillators form a scale-free network with degree exponent $lambda$. An oscillator of degree $k_i$ is coupled to its neighboring oscillators with asymmetric and degree-dependent coupling in the form of $couplingcoeff k_i^{eta-1}$. By invoking the mean-field approach, we determine the synchronization transition point $J_c$, which is zero (finite) when $eta > lambda-2$ ($eta < lambda-2$). We find eight different synchronization transition behaviors depending on the values of $eta$ and $lambda$, and derive the critical exponents associated with the order parameter and the finite-size scaling in each case. The synchronization transition is also studied from the perspective of cluster formation of synchronized vertices. The cluster-size distribution and the largest cluster size as a function of the system size are derived for each case using the generating function technique. Our analytic results are confirmed by numerical simulations.
Source arXiv, cond-mat/0606048
Other source [GID 577341] pmid17358107
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