{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,5]],"date-time":"2026-02-05T22:50:35Z","timestamp":1770331835798,"version":"3.49.0"},"reference-count":15,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2021,12,16]],"date-time":"2021-12-16T00:00:00Z","timestamp":1639612800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11871131"],"award-info":[{"award-number":["11871131"]}],"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":["12031002"],"award-info":[{"award-number":["12031002"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022,3,2]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>This paper investigates the behaviour of infinite chains of kinematic points described by scalar Laurent operators with first\/second-order linear differential equations. Some conditions on the initial states of these infinite chains are given to ensure that the corresponding solutions converge. In particular, a necessary and sufficient condition for the convergence of the first-order system is derived by using ergodic theory.<\/jats:p>","DOI":"10.1093\/imamci\/dnab036","type":"journal-article","created":{"date-parts":[[2021,11,12]],"date-time":"2021-11-12T12:13:58Z","timestamp":1636719238000},"page":"93-111","source":"Crossref","is-referenced-by-count":1,"title":["Behaviour of infinite chains described by Laurent operators: first\/second-order equations"],"prefix":"10.1093","volume":"39","author":[{"given":"Dongmei","family":"Liu","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Dalian University of Technology, Dalian City, Liaoning Province, 116024, China"}]},{"given":"Liu","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Dalian University of Technology, Dalian City, Liaoning Province, 116024, China"}]},{"given":"Yufeng","family":"Lu","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Dalian University of Technology, Dalian City, Liaoning Province, 116024, China"}]}],"member":"286","published-online":{"date-parts":[[2021,12,16]]},"reference":[{"key":"2022030217385922900_ref1","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1016\/j.sysconle.2016.03.005","article-title":"\u2113\u221e-stability analysis of discrete autonomous systems described by Laurent polynomial matrix operators","volume":"93","author":"Athalye","year":"2016","journal-title":"Systems Control Lett."},{"key":"2022030217385922900_ref2","doi-asserted-by":"crossref","first-page":"2929","DOI":"10.1109\/TAC.2019.2936409","article-title":"Behavior of n infinite chains of kinematic points with the immediate-neighbors interaction dynamics","volume":"65","author":"Athalye","year":"2020","journal-title":"IEEE Transactions on Automatic Control"},{"key":"2022030217385922900_ref3","doi-asserted-by":"crossref","first-page":"768","DOI":"10.1109\/TAC.2020.2976297","article-title":"Comparison between different notions of stability for Laurent systems","volume":"66","author":"Athalye","year":"2021","journal-title":"IEEE Transactions on Automatic Control"},{"key":"2022030217385922900_ref4","doi-asserted-by":"crossref","first-page":"1091","DOI":"10.1109\/TAC.2002.800646","article-title":"Distributed control of spatially invariant systems","volume":"47","author":"Bamieh","year":"2002","journal-title":"IEEE Transactions on Automatic Control"},{"key":"2022030217385922900_ref5","doi-asserted-by":"crossref","first-page":"853","DOI":"10.4171\/JEMS\/605","article-title":"Fine scales of decay of operator semigroups, Journal of the European Mathematical Society","volume":"18","author":"Batty","year":"2016","journal-title":"JEMS"},{"key":"2022030217385922900_ref6","doi-asserted-by":"crossref","first-page":"519","DOI":"10.1112\/blms\/bdw024","article-title":"Quantified versions of Ingham\u2019s theorem","volume":"48","author":"Chill","year":"2016","journal-title":"Bulletin of the London Mathematical Society"},{"key":"2022030217385922900_ref7","doi-asserted-by":"crossref","first-page":"1478","DOI":"10.1109\/TAC.2003.816954","article-title":"Distributed control design for spatially interconnected systems","volume":"48","author":"D\u2019Andrea","year":"2003","journal-title":"IEEE Transactions on Automatic Control, North-Holland"},{"key":"2022030217385922900_ref8","doi-asserted-by":"crossref","first-page":"463","DOI":"10.1007\/s00498-014-0125-y","article-title":"Asymptotic behaviour of infinite chains of coupled kinematic points: second-order equations","volume":"26","author":"Feintuch","year":"2014","journal-title":"Math. 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