{"paper":{"title":"Analytical foundation for adversarial synchronization control in oscillator networks","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Adversarial kicks in Kuramoto oscillator networks produce a finite, coupling-independent increment in the synchronization order parameter.","cross_cats":["physics.soc-ph"],"primary_cat":"nlin.AO","authors_text":"Kazuhiro Takemoto","submitted_at":"2026-05-14T07:31:14Z","abstract_excerpt":"This study provides an analytical foundation for adversarial synchronization control in Kuramoto oscillator networks, where small gradient-based perturbations applied repeatedly to oscillator phases can dramatically enhance or suppress collective synchronization. Using the Ott--Antonsen reduction, we derive an exact closed-form expression for the effect of a single adversarial perturbation (kick) on the order parameter. A key finding is that each kick produces a finite, coupling-independent increment in the order parameter even when synchronization is arbitrarily weak, which combined with slow"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"each kick produces a finite, coupling-independent increment in the order parameter even when synchronization is arbitrarily weak, which combined with slow relaxation near the critical coupling and mean-field feedback explains the disproportionate amplification previously observed in numerical simulations","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The Ott-Antonsen reduction remains valid for the perturbed system and that the annealed network approximation accurately captures the synchronization behavior of representative model networks","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Derives exact closed-form increment to the order parameter from each adversarial kick in Kuramoto networks, independent of coupling strength, using Ott-Antonsen reduction.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Adversarial kicks in Kuramoto oscillator networks produce a finite, coupling-independent increment in the synchronization order parameter.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"1731a8fdbe927835b8bda2f30f5aea592efeb50c29ace7115f2c21d5c907adb0"},"source":{"id":"2605.14492","kind":"arxiv","version":1},"verdict":{"id":"c0d70e3a-3812-496f-9812-43f7c0fce8ba","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T01:32:08.086223Z","strongest_claim":"each kick produces a finite, coupling-independent increment in the order parameter even when synchronization is arbitrarily weak, which combined with slow relaxation near the critical coupling and mean-field feedback explains the disproportionate amplification previously observed in numerical simulations","one_line_summary":"Derives exact closed-form increment to the order parameter from each adversarial kick in Kuramoto networks, independent of coupling strength, using Ott-Antonsen reduction.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The Ott-Antonsen reduction remains valid for the perturbed system and that the annealed network approximation accurately captures the synchronization behavior of representative model networks","pith_extraction_headline":"Adversarial kicks in Kuramoto oscillator networks produce a finite, coupling-independent increment in the synchronization order parameter."},"references":{"count":30,"sample":[{"doi":"","year":2008,"title":"Physics reports , volume=","work_id":"35e08f48-e688-4222-94a8-7939c3e9f8f5","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2014,"title":"Synchronization in complex networks of phase oscillators: A survey , author=. 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