{"paper":{"title":"Synchronization transition of heterogeneously coupled oscillators on scale-free networks","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"B. Kahng, D. Kim, D.-S. Lee, E. Oh","submitted_at":"2006-06-02T02:30:38Z","abstract_excerpt":"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 de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0606048","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}