{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T19:52:25Z","timestamp":1790797945442,"version":"4.1.0"},"reference-count":38,"publisher":"World Scientific Pub Co Pte Ltd","issue":"13","funder":[{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","award":["R2686A02"],"award-info":[{"award-number":["R2686A02"]}],"id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2022,10]]},"abstract":"<jats:p> In this paper, we apply bifurcation theory to consider four predator\u2013prey systems which include the Allee effect, and show that the species having a strong Allee effct may affect their predation and hence extinction risk. It is shown that the models with the Allee effect exhibit more complex dynamical behaviors compared with that without the Allee effect. In particular, two models with no Allee effect do not have Hopf bifurcation, but can have Hopf bifurcation with the Allee effect; and one model, which does not have Bogdanov\u2013Takens bifurcation if no Allee effect is involved, can have Bogdanov\u2013Takens bifurcation of codimension two. Especially, for one model with Holling type II functional response of the predator to the prey, the Allee effect not only completely changes the stability of the equilibrium at the origin, but also changes the supercritical Hopf bifurcation arising from an interior equilibrium to subcritical Hopf bifurcation with very limited parameter values to yield unstable limit cycles, and further increases the system\u2019s stability. <\/jats:p>","DOI":"10.1142\/s0218127422502030","type":"journal-article","created":{"date-parts":[[2022,11,3]],"date-time":"2022-11-03T06:40:11Z","timestamp":1667457611000},"source":"Crossref","is-referenced-by-count":12,"title":["Complex Dynamics of Predator\u2013Prey Systems with Allee Effect"],"prefix":"10.1142","volume":"32","author":[{"given":"Yanni","family":"Zeng","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics, Western University, London, Ontario, Canada N6A 5B7, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8848-0584","authenticated-orcid":false,"given":"Pei","family":"Yu","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, Western University, London, Ontario, Canada N6A 5B7, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"219","published-online":{"date-parts":[[2022,11,3]]},"reference":[{"key":"S0218127422502030BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/S0169-5347(00)01908-X"},{"key":"S0218127422502030BIB002","volume-title":"Animal Aggregations: A Study in General Sociology","author":"Allee W. C.","year":"1932"},{"key":"S0218127422502030BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-5193(89)80211-5"},{"key":"S0218127422502030BIB004","series-title":"World Sci. Ser. Nonlinear Sci. Ser. A.","volume-title":"Nonlinear Dynamics of Interaction Populations","volume":"11","author":"Bazykin A. D.","year":"1988"},{"key":"S0218127422502030BIB005","doi-asserted-by":"publisher","DOI":"10.1017\/S0143385700004119"},{"key":"S0218127422502030BIB006","volume-title":"Deterministic Mathematical Models in Population Ecology","author":"Freedman H. I.","year":"1980"},{"key":"S0218127422502030BIB007","volume-title":"The Struggle for Existence","author":"Gause G. G.","year":"1969"},{"key":"S0218127422502030BIB008","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127410027830"},{"key":"S0218127422502030BIB009","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2011.09.043"},{"key":"S0218127422502030BIB010","doi-asserted-by":"publisher","DOI":"10.3934\/dcds.2015.35.205"},{"key":"S0218127422502030BIB011","volume-title":"Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields","author":"Guckenheimer J.","year":"1993","edition":"4"},{"key":"S0218127422502030BIB012","doi-asserted-by":"publisher","DOI":"10.4039\/Ent91385-7"},{"key":"S0218127422502030BIB013","doi-asserted-by":"publisher","DOI":"10.4039\/entm9745fv"},{"key":"S0218127422502030BIB014","doi-asserted-by":"publisher","DOI":"10.1007\/s002850100079"},{"key":"S0218127422502030BIB015","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2014.04.024"},{"key":"S0218127422502030BIB016","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127417500432"},{"key":"S0218127422502030BIB017","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127420501291"},{"key":"S0218127422502030BIB018","doi-asserted-by":"publisher","DOI":"10.1007\/s002850050105"},{"key":"S0218127422502030BIB019","first-page":"325","volume":"21","author":"Kuang Y.","year":"1999","journal-title":"Fields Inst. Commun."},{"key":"S0218127422502030BIB020","doi-asserted-by":"publisher","DOI":"10.1137\/060662460"},{"key":"S0218127422502030BIB021","doi-asserted-by":"publisher","DOI":"10.3934\/dcdsb.2015.20.1107"},{"key":"S0218127422502030BIB022","volume-title":"Elements of Physical Biology","author":"Lotka A. J.","year":"1925"},{"key":"S0218127422502030BIB023","doi-asserted-by":"publisher","DOI":"10.1016\/j.mbs.2008.12.008"},{"key":"S0218127422502030BIB024","doi-asserted-by":"publisher","DOI":"10.1007\/b98868"},{"key":"S0218127422502030BIB025","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127414501065"},{"key":"S0218127422502030BIB026","doi-asserted-by":"publisher","DOI":"10.1007\/s11538-018-0394-6"},{"key":"S0218127422502030BIB027","doi-asserted-by":"publisher","DOI":"10.1038\/118558a0"},{"key":"S0218127422502030BIB028","doi-asserted-by":"publisher","DOI":"10.1007\/s002850100097"},{"key":"S0218127422502030BIB029","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2005.11.048"},{"key":"S0218127422502030BIB030","doi-asserted-by":"publisher","DOI":"10.1006\/jsvi.1997.1347"},{"key":"S0218127422502030BIB031","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127499001401"},{"key":"S0218127422502030BIB032","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/16\/1\/317"},{"key":"S0218127422502030BIB033","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2015.12.022"},{"key":"S0218127422502030BIB034","doi-asserted-by":"publisher","DOI":"10.1007\/s00332-019-09550-7"},{"key":"S0218127422502030BIB035","first-page":"3253","volume":"13","author":"Zeng B.","year":"2020","journal-title":"Discr. Contin. Dyn. Syst. Ser. S"},{"key":"S0218127422502030BIB036","series-title":"Translations of Mathematical Monographs","volume-title":"Qualitative Theory of Differential Equations.","volume":"101","author":"Zhang Z.","year":"1991"},{"key":"S0218127422502030BIB037","doi-asserted-by":"publisher","DOI":"10.1137\/120884535"},{"key":"S0218127422502030BIB038","doi-asserted-by":"publisher","DOI":"10.1137\/130937421"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127422502030","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,11,3]],"date-time":"2022-11-03T06:43:10Z","timestamp":1667457790000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0218127422502030"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,10]]},"references-count":38,"journal-issue":{"issue":"13","published-print":{"date-parts":[[2022,10]]}},"alternative-id":["10.1142\/S0218127422502030"],"URL":"https:\/\/doi.org\/10.1142\/s0218127422502030","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,10]]},"article-number":"2250203"}}