Abstract
We investigate the synchronization transition of the modified Kuramoto model where the oscillators form a scale-free network with degree exponent . An oscillator of degree is coupled to its neighboring oscillators with asymmetric and degree-dependent coupling in the form of . By invoking the mean-field approach, we find eight different synchronization transition behaviors depending on the values of and , and derive the critical exponents associated with the order parameter and the finite-size scaling in each case. The synchronization transition point is determined as being zero (finite) when . 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.
- Received 1 June 2006
DOI:https://doi.org/10.1103/PhysRevE.75.011104
©2007 American Physical Society