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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 | Abstract: | We 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 | Services: | Forum | Review | PDF | Favorites |
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