{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T12:29:48Z","timestamp":1787228988914,"version":"build-2736575974"},"reference-count":49,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11475253"],"award-info":[{"award-number":["11475253"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11605142"],"award-info":[{"award-number":["11605142"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Appl. Dyn. Syst."],"published-print":{"date-parts":[[2017,1]]},"abstract":"<jats:p>Synchronization (or sync) is a basic problem in nature and engineering. One decade ago, the problem of the size of the sync (as a global geometric quantity) was first proposed by Wiley, Strogatz, and Girvan (WSG). In studying a ring of $N$ coupled identical phase oscillators with each interacting equally with its $d$ nearest neighbors on either side, they found that the sync state becomes globally stable when $d\/N$ is greater than a critical constant [D. A. Wiley, S. H. Strogatz, and M. Girvan, Chaos, 16 (2006) 015103]. Based on our previous results on the local stability of splay states in a ring of coupled Landau--Stuart oscillators, in this paper we further study the problem of global stability of the sync with amplitude effects, and we find that for any sufficiently large $N$ the condition for the critical coupling range $d_c$ satisfying global stability of sync now becomes $d_c \\propto N^ \\gamma$ ($\\gamma=2\/3$), whereas when the coupling strength becomes weaker, the condition gradually changes to $d_c \\simeq 0.3405N$ coincidental with the former result of the WSG in coupled phase oscillators. These relations are indicative of the favorable effect of amplitude for global stability of the sync. All these findings are based on rigorous theoretical analysis and have been well verified by numerical simulation; they are expected to be of potential significance for theory as well as application of synchronization in networked oscillatory systems.<\/jats:p>","DOI":"10.1137\/16m1086005","type":"journal-article","created":{"date-parts":[[2017,10,12]],"date-time":"2017-10-12T11:17:42Z","timestamp":1507807062000},"page":"1923-1945","source":"Crossref","is-referenced-by-count":4,"title":["Global Stability of the Sync with Amplitude Effects"],"prefix":"10.1137","volume":"16","author":[{"given":"Shuai","family":"Liu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wei","family":"Zou","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"MiaoZhuang","family":"He","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J\u00fcrgen","family":"Kurths","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Meng","family":"Zhan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2017,10,12]]},"reference":[{"key":"atypb1","doi-asserted-by":"crossref","unstructured":"Y. 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