{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T11:28:58Z","timestamp":1787225338164,"version":"build-2736575974"},"reference-count":54,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","funder":[{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["CUSF-DH-T-2024065"],"award-info":[{"award-number":["CUSF-DH-T-2024065"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12001096"],"award-info":[{"award-number":["12001096"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100007219","name":"Natural Science Foundation of Shanghai Municipality","doi-asserted-by":"publisher","award":["24ZR1401900"],"award-info":[{"award-number":["24ZR1401900"]}],"id":[{"id":"10.13039\/100007219","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Appl. Math."],"published-print":{"date-parts":[[2026,2,28]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>In this paper, we investigate the conditions under which the periodic orbits cannot exist in high-dimensional Lotka\u2013Volterra systems. By employing the geometric approach of surface functionals developed by Li and Muldowney and by Smale\u2019s embedding theory, we derive criteria that preclude the existence of periodic orbits in [Formula: see text]-dimensional Lotka\u2013Volterra systems with [Formula: see text]. These criteria are the first to rule out periodic orbits in high-dimensional Lotka\u2013Volterra systems using the geometric approach of Li and Muldowney. Notably, for the three-dimensional case ([Formula: see text]), our results generalize the criterion derived by van den Driessche and Zeeman [ SIAM J. Appl. Math., 58 (1998), pp.\u00a0227\u2013234] for competitive Lotka\u2013Volterra systems, encompassing it as a special case. Furthermore, when combined with the assumption of permanence, our conditions imply the existence of a globally asymptotically stable positive equilibrium. The results are illustrated with ecological examples.<\/jats:p>","DOI":"10.1137\/25m1783163","type":"journal-article","created":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T08:25:46Z","timestamp":1770971146000},"page":"410-426","source":"Crossref","is-referenced-by-count":0,"title":["The \\({n}\\)-Dimensional General Lotka\u2013Volterra System with No Periodic Orbits"],"prefix":"10.1137","volume":"86","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3343-1726","authenticated-orcid":true,"given":"Lei","family":"Niu","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Donghua University, Shanghai 201620, People\u2019s Republic of China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-5787-9293","authenticated-orcid":true,"given":"Ying","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Donghua University, Shanghai 201620, People\u2019s Republic of China."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2026,2,13]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1137\/S0036139902413829"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01832841"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1007\/s00285-005-0333-7"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1007\/BF00318088"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1016\/0375-9601(88)90920-6"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1007\/BF00178776"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.1993.1037"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1126\/science.208.4440.173"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1137\/15M1006878"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1137\/S0036139994272060"},{"key":"ref11","volume-title":"Stability and Asymptotic Behavior of Differential Equations","author":"Coppel W. 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