{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"5d4bd77f81015ae5706a7487dee9016e460532e00f1ad4d1e08dc814893471ba","created":"2026-10-03T07:18:11Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"d64dfc6dd9b667829cb2793db0c0498da32186b1e5bea99e1ef825a3e2b41a97","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"stat.synchronization-networks.chimera-lifetime","kind":"well-posed","literature_status":"partially-resolved","n":"1","parents":[],"plain":"A chimera state is a pattern in which identical oscillators split into a synchronized group and an unsynchronized group. In infinite systems it can last forever, but in finite ones it eventually collapses, and how its lifetime grows with size is known only numerically.","posed_since":"2011","precise":"For rings of $N$ identical phase oscillators with nonlocal coupling (Kuramoto-Battogtokh kernel, phase lag $\\alpha$) and for two-population models, determine the mean chimera lifetime as a function of $N$ and $\\alpha$, testing the reported exponential growth $\\tau \\sim \\exp(c N)$, and identify the collapse mechanism. An answer is a derived law $\\tau(N, \\alpha)$ matching simulations.","problem_ref":null,"references":"","settled_by":"A large-deviation or escape-rate computation of $c(\\alpha)$ that agrees with direct simulations over a range of $N$.","status_note":"Exponential growth of the lifetime with N was reported numerically in 2011 for ring networks; no derivation of the rate c exists.","title":"Lifetime of chimera states in finite oscillator 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