Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2004-11-08
Physical Review E 71, 036151 (2005)
Physics
Condensed Matter
Disordered Systems and Neural Networks
To appear in PRE; Added an Appendix, a reference, modified two figures and improved the discussion of the range of validity of
Scientific paper
10.1103/PhysRevE.71.036151
We study the transition from incoherence to coherence in large networks of coupled phase oscillators. We present various approximations that describe the behavior of an appropriately defined order parameter past the transition, and generalize recent results for the critical coupling strength. We find that, under appropriate conditions, the coupling strength at which the transition occurs is determined by the largest eigenvalue of the adjacency matrix. We show how, with an additional assumption, a mean field approximation recently proposed is recovered from our results. We test our theory with numerical simulations, and find that it describes the transition when our assumptions are satisfied. We find that our theory describes the transition well in situations in which the mean field approximation fails. We study the finite size effects caused by nodes with small degree and find that they cause the critical coupling strength to increase.
Hunt Brian R.
Ott Edward
Restrepo Juan G.
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