{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,30]],"date-time":"2026-01-30T09:15:59Z","timestamp":1769764559925,"version":"3.49.0"},"reference-count":44,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2022,6,20]],"date-time":"2022-06-20T00:00:00Z","timestamp":1655683200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Educational and scientific research projects for young and middle-aged teachers of Fujian Province (Science and Technology)","award":["JAT200690"],"award-info":[{"award-number":["JAT200690"]}]},{"name":"Educational and scientific research projects for young and middle-aged teachers of Fujian Province (Science and Technology)","award":["2019J01841"],"award-info":[{"award-number":["2019J01841"]}]},{"name":"Educational and scientific research projects for young and middle-aged teachers of Fujian Province (Science and Technology)","award":["2021J011155"],"award-info":[{"award-number":["2021J011155"]}]},{"name":"Natural Science Foundation of Fujian Province","award":["JAT200690"],"award-info":[{"award-number":["JAT200690"]}]},{"name":"Natural Science Foundation of Fujian Province","award":["2019J01841"],"award-info":[{"award-number":["2019J01841"]}]},{"name":"Natural Science Foundation of Fujian Province","award":["2021J011155"],"award-info":[{"award-number":["2021J011155"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>A two species obligate commensal symbiosis model with Crowley\u2013Martin functional response was proposed and studied in this paper. For an autonomous case, local and global dynamic behaviors of the system were investigated, respectively. The conditions that ensure the existence of the positive equilibrium is coincidentla to the conditions of global stability of a positive equilibrium. For nonautonomous cases, persistent and extinction properties of the system are investigated.<\/jats:p>","DOI":"10.3390\/axioms11060298","type":"journal-article","created":{"date-parts":[[2022,6,21]],"date-time":"2022-06-21T01:43:27Z","timestamp":1655775807000},"page":"298","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Dynamic Behaviors of an Obligate Commensal Symbiosis Model with Crowley\u2013Martin Functional Responses"],"prefix":"10.3390","volume":"11","author":[{"given":"Lili","family":"Xu","sequence":"first","affiliation":[{"name":"College of Mathematics and Physics, Ningde Normal University, Ningde 352000, China"}]},{"given":"Yalong","family":"Xue","sequence":"additional","affiliation":[{"name":"College of Mathematics and Physics, Ningde Normal University, Ningde 352000, China"}]},{"given":"Xiangdong","family":"Xie","sequence":"additional","affiliation":[{"name":"College of Mathematics and Physics, Ningde Normal University, Ningde 352000, China"}]},{"given":"Qifa","family":"Lin","sequence":"additional","affiliation":[{"name":"College of Mathematics and Physics, Ningde Normal University, Ningde 352000, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,6,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1186\/s13662-019-2209-y","article-title":"The influence of partial closure for the populations to a non-selective harvesting Lotka-Volterra discrete amensalism model","volume":"2019","author":"Su","year":"2019","journal-title":"Adv. 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