{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,24]],"date-time":"2025-09-24T09:07:31Z","timestamp":1758704851636,"version":"3.37.3"},"reference-count":29,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2021,4,13]],"date-time":"2021-04-13T00:00:00Z","timestamp":1618272000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,4,13]],"date-time":"2021-04-13T00:00:00Z","timestamp":1618272000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007162","name":"Guangdong Science and Technology Department","doi-asserted-by":"publisher","award":["2020A1414010119"],"award-info":[{"award-number":["2020A1414010119"]}],"id":[{"id":"10.13039\/501100007162","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12071095"],"award-info":[{"award-number":["12071095"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J. Appl. Math. Comput."],"published-print":{"date-parts":[[2022,4]]},"DOI":"10.1007\/s12190-021-01551-8","type":"journal-article","created":{"date-parts":[[2021,4,13]],"date-time":"2021-04-13T11:06:11Z","timestamp":1618311971000},"page":"767-794","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Uniform persistence and multistability in a two-predator\u2013one-prey system with inter-specific and intra-specific competition"],"prefix":"10.1007","volume":"68","author":[{"given":"Yuhua","family":"Long","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7215-8750","authenticated-orcid":false,"given":"Lin","family":"Wang","sequence":"additional","affiliation":[]},{"given":"Jia","family":"Li","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,4,13]]},"reference":[{"key":"1551_CR1","volume-title":"Elements of Physical Biology","author":"AJ Lotka","year":"1925","unstructured":"Lotka, A.J.: Elements of Physical Biology. Williams and Wilkins, Baltimore (1925)"},{"key":"1551_CR2","unstructured":"Volterra, V.: Variazionie fluttuazioni del numero d\u2019individui in specie animali conviventi. Mem. Acad. Lincei. 2, 31\u2013113 (1925) (Variations and fluctuations of a number of individuals in animal species living together. Translation In: R.N. Chapman: Animal Ecology. New York: McGraw Hill 1931, pp. 409\u2013448)"},{"key":"1551_CR3","volume-title":"Complex Population Dynamics: A Theoretical\/Empirical Synthesis","author":"P Turchin","year":"2003","unstructured":"Turchin, P.: Complex Population Dynamics: A Theoretical\/Empirical Synthesis. Princeton University Press, Princeton (2003)"},{"key":"1551_CR4","doi-asserted-by":"publisher","first-page":"5","DOI":"10.4039\/entm9745fv","volume":"45","author":"CS Holling","year":"1965","unstructured":"Holling, C.S.: The functional response of predator to prey density and its role in mimicry and population regulations. Mem. Entomol. Soc. Can. 45, 5\u201360 (1965)","journal-title":"Mem. Entomol. Soc. Can."},{"key":"1551_CR5","doi-asserted-by":"publisher","first-page":"331","DOI":"10.2307\/3866","volume":"44","author":"JR Beddington","year":"1975","unstructured":"Beddington, J.R.: Mutual interference between parasites or predators and its effect on searching efficiency. J. Anim. Ecol. 44, 331\u2013340 (1975)","journal-title":"J. Anim. Ecol."},{"key":"1551_CR6","doi-asserted-by":"publisher","first-page":"881","DOI":"10.2307\/1936298","volume":"56","author":"DL DeAngelis","year":"1975","unstructured":"DeAngelis, D.L., Goldstein, R.A., O\u2019Neill, R.V.: A model for trophic interaction. Ecology 56, 881\u2013892 (1975)","journal-title":"Ecology"},{"key":"1551_CR7","doi-asserted-by":"publisher","first-page":"289","DOI":"10.1086\/283161","volume":"111","author":"L Real","year":"1977","unstructured":"Real, L.: The kinetics of functional response. Am. Nat. 111, 289\u2013300 (1977)","journal-title":"Am. Nat."},{"key":"1551_CR8","doi-asserted-by":"publisher","first-page":"965","DOI":"10.1007\/s10884-019-09755-0","volume":"32","author":"W Ding","year":"2020","unstructured":"Ding, W., Huang, W.: Global dynamics of a predator\u2013prey model with general Holling type functional responses. J. Dyn. Differ. Equ. 32, 965\u2013978 (2020)","journal-title":"J. Dyn. Differ. Equ."},{"key":"1551_CR9","doi-asserted-by":"publisher","first-page":"243","DOI":"10.1137\/0129022","volume":"29","author":"RM May","year":"1975","unstructured":"May, R.M., Leonard, W.J.: Nonlinear aspects of competition between three species. SIAM J. Appl. Math. 29, 243\u2013253 (1975)","journal-title":"SIAM J. Appl. Math."},{"key":"1551_CR10","doi-asserted-by":"publisher","first-page":"127","DOI":"10.1086\/283257","volume":"112","author":"H Caswell","year":"1978","unstructured":"Caswell, H.: Predator-mediated coexistence: a nonequilibrium model. Am. Nat. 112, 127\u2013154 (1978)","journal-title":"Am. Nat."},{"key":"1551_CR11","doi-asserted-by":"publisher","first-page":"285","DOI":"10.1007\/BF00276227","volume":"44","author":"V Hutson","year":"1985","unstructured":"Hutson, V., Law, R.: Permanent coexistence in general models of three interacting species. J. Math. Biol. 44, 285\u2013298 (1985)","journal-title":"J. Math. Biol."},{"key":"1551_CR12","doi-asserted-by":"publisher","first-page":"763","DOI":"10.1137\/S0036139993253201","volume":"55","author":"SB Hsu","year":"1995","unstructured":"Hsu, S.B., Hwang, T.W.: Global stability for a class of predator\u2013prey systems. SIAM J. Appl. Math. 55, 763\u2013783 (1995)","journal-title":"SIAM J. Appl. Math."},{"key":"1551_CR13","doi-asserted-by":"publisher","DOI":"10.1515\/9780691206912","volume-title":"Stability and Complexity in Ecosystems","author":"RM May","year":"2001","unstructured":"May, R.M.: Stability and Complexity in Ecosystems. Princeton University Press, Princeton (2001)"},{"key":"1551_CR14","doi-asserted-by":"publisher","first-page":"1580","DOI":"10.1137\/070702485","volume":"69","author":"Y Xia","year":"2009","unstructured":"Xia, Y., Han, M.: New conditions on the existence and stability of periodic solution in a Lokta\u2013Volterra\u2019s population system. SIAM J. Appl. Math. 69, 1580\u20131597 (2009)","journal-title":"SIAM J. Appl. Math."},{"key":"1551_CR15","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s12190-018-01236-9","volume":"61","author":"P Mishra","year":"2019","unstructured":"Mishra, P., Raw, S.N.: Dynamical complexities in a predator\u2013prey system involving teams of two prey and one predator. J. Appl. Math. Comput. 61, 1\u201324 (2019)","journal-title":"J. Appl. Math. Comput."},{"key":"1551_CR16","doi-asserted-by":"publisher","first-page":"213","DOI":"10.1016\/0025-5564(84)90032-4","volume":"68","author":"HI Freedman","year":"1984","unstructured":"Freedman, H.I., Waltman, P.: Persistence in models of three interacting predator\u2013prey populations. Math. Biosci. 68, 213\u2013231 (1984)","journal-title":"Math. Biosci."},{"key":"1551_CR17","doi-asserted-by":"publisher","first-page":"808","DOI":"10.1016\/j.biosystems.2007.04.003","volume":"90","author":"S Gakkhar","year":"2007","unstructured":"Gakkhar, S., Singh, B., Naji, R.K.: Dynamical behavior of two predators competing over a single prey. Biosystems 90, 808\u2013817 (2007)","journal-title":"Biosystems"},{"key":"1551_CR18","doi-asserted-by":"publisher","first-page":"307","DOI":"10.15388\/NA.2004.9.4.15147","volume":"9","author":"B Dubey","year":"2004","unstructured":"Dubey, B., Upadhyay, R.K.: Persistence and extinction of one-prey and two-predators system. Nonlinear Anal. Model. Control 9, 307\u2013329 (2004)","journal-title":"Nonlinear Anal. Model. Control"},{"key":"1551_CR19","first-page":"943","volume":"6","author":"J Alebraheem","year":"2012","unstructured":"Alebraheem, J., Abu-Hasan, Y.: Persistence of predators in a two predators-one prey model with non-periodic solution. Appl. Math. Sci. 6, 943\u2013956 (2012)","journal-title":"Appl. Math. Sci."},{"key":"1551_CR20","doi-asserted-by":"publisher","first-page":"353","DOI":"10.2307\/5465","volume":"60","author":"I Hanski","year":"1991","unstructured":"Hanski, I., Hansson, L., Henttonen, H.: Specialist predators, generalist predators, and the microtine rodent cycle. J. Anim. Ecol. 60, 353\u2013367 (1991)","journal-title":"J. Anim. Ecol."},{"key":"1551_CR21","volume-title":"An Introduction to Mathematical Ecology","author":"EC Pielou","year":"1970","unstructured":"Pielou, E.C.: An Introduction to Mathematical Ecology. Wiley, New York (1970)"},{"key":"1551_CR22","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1016\/j.mbs.2013.07.021","volume":"246","author":"M Haque","year":"2013","unstructured":"Haque, M., Ali, N., Chakravarty, S.: Study of a tri-trophic prey-dependent food chain model of interacting populations. Math. Biosci. 246, 55\u201371 (2013)","journal-title":"Math. Biosci."},{"key":"1551_CR23","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611970432","volume-title":"The Stability of Dynamical Systems. Regional Conference Series in Applied Mathematics","author":"J.P LaSalle","year":"1976","unstructured":"LaSalle, J..P.: The Stability of Dynamical Systems. Regional Conference Series in Applied Mathematics. SIAM, Philadelphia (1976)"},{"key":"1551_CR24","doi-asserted-by":"publisher","first-page":"267","DOI":"10.1007\/BF01540776","volume":"98","author":"V Hutson","year":"1984","unstructured":"Hutson, V.: A theorem on average Liapunov functions. Mh. Math. 98, 267\u2013275 (1984)","journal-title":"Mh. Math."},{"key":"1551_CR25","volume-title":"Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering","author":"SH Strogatz","year":"2019","unstructured":"Strogatz, S.H.: Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering, 2nd edn. CRC Press, New York (2019)","edition":"2"},{"key":"1551_CR26","doi-asserted-by":"publisher","first-page":"1033","DOI":"10.1216\/rmjm\/1181073060","volume":"20","author":"V Hutson","year":"1990","unstructured":"Hutson, V.: The existence of an equilibrium for permanent systems. Rocky Mt. J. Math. 20, 1033\u20131040 (1990)","journal-title":"Rocky Mt. J. Math."},{"key":"1551_CR27","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-56433-3","volume-title":"Dynamical Systems in Population Biology","author":"X-Q Zhao","year":"2017","unstructured":"Zhao, X.-Q.: Dynamical Systems in Population Biology, 2nd edn. Springer, New York (2017)","edition":"2"},{"key":"1551_CR28","doi-asserted-by":"publisher","first-page":"701","DOI":"10.1007\/s10867-013-9327-7","volume":"39","author":"S Sarwardi","year":"2013","unstructured":"Sarwardi, S., Mandal, P.K., Ray, S.: Dynamical behaviour of a two-predator model with prey refuge. J. Biol. Phys. 39, 701\u2013722 (2013)","journal-title":"J. Biol. Phys."},{"key":"1551_CR29","doi-asserted-by":"publisher","first-page":"1292","DOI":"10.1126\/science.131.3409.1292","volume":"131","author":"G Hardin","year":"1960","unstructured":"Hardin, G.: The competitive exclusion principle. Science 131, 1292\u20131297 (1960)","journal-title":"Science"}],"container-title":["Journal of Applied Mathematics and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-021-01551-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s12190-021-01551-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-021-01551-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,3,17]],"date-time":"2022-03-17T17:25:19Z","timestamp":1647537919000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s12190-021-01551-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,4,13]]},"references-count":29,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2022,4]]}},"alternative-id":["1551"],"URL":"https:\/\/doi.org\/10.1007\/s12190-021-01551-8","relation":{},"ISSN":["1598-5865","1865-2085"],"issn-type":[{"type":"print","value":"1598-5865"},{"type":"electronic","value":"1865-2085"}],"subject":[],"published":{"date-parts":[[2021,4,13]]},"assertion":[{"value":"11 January 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 March 2021","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 April 2021","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 April 2021","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}