{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,9]],"date-time":"2026-02-09T23:43:41Z","timestamp":1770680621991,"version":"3.49.0"},"reference-count":31,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2021,11,26]],"date-time":"2021-11-26T00:00:00Z","timestamp":1637884800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11971076"],"award-info":[{"award-number":["11971076"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>One fundamental step towards grasping the global dynamic structure of a population system involves characterizing the convergence behavior (specifically, how to characterize the convergence behavior). This paper focuses on the neutral functional differential equations arising from population dynamics. With the help of monotonicity techniques and functional methods, we analyze the subtle relations of both the \u03c9-limited set and special point. Meanwhile, we prove that every bounded solution converges to a constant vector, as t tends to positive infinity. Our results correlate with the findings from earlier publications, and our proof yields an improved Haddock conjecture.<\/jats:p>","DOI":"10.3390\/sym13122252","type":"journal-article","created":{"date-parts":[[2021,12,1]],"date-time":"2021-12-01T03:12:40Z","timestamp":1638328360000},"page":"2252","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Convergence on Population Dynamics and High-Dimensional Haddock Conjecture"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9401-6614","authenticated-orcid":false,"given":"Wenke","family":"Wang","sequence":"first","affiliation":[{"name":"College of Meteorology and Oceanography, National University of Defense Technology, Changsha 410073, China"}]},{"given":"Le","family":"Li","sequence":"additional","affiliation":[{"name":"College of Meteorology and Oceanography, National University of Defense Technology, Changsha 410073, China"}]},{"given":"Xuejun","family":"Yi","sequence":"additional","affiliation":[{"name":"School of Mathematics, Hunan University, Changsha 410082, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0732-226X","authenticated-orcid":false,"given":"Chuangxia","family":"Huang","sequence":"additional","affiliation":[{"name":"Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science and Technology, Changsha 410114, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,11,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Wu, J., and Zhang, X. 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