{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T06:16:48Z","timestamp":1780381008231,"version":"3.54.1"},"reference-count":46,"publisher":"World Scientific Pub Co Pte Ltd","issue":"06","funder":[{"name":"University Grants Commission, India","award":["2061441029"],"award-info":[{"award-number":["2061441029"]}]},{"name":"University Grants Commission, India","award":["427219"],"award-info":[{"award-number":["427219"]}]},{"name":"RUDN University Program","award":["5-100"],"award-info":[{"award-number":["5-100"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2020,5]]},"abstract":"<jats:p>Prey\u2013predator models are building blocks for many food-chain and food-web models in theoretical population biology. These models can be divided into two groups depending on the nature of predators, namely, specialist predator and generalist predator. Generalist predators can survive in the absence of prey but specialist predators go to extinction. Prey\u2013predator models with specialist predator and Allee effect in prey growth have been investigated by several researchers and various types of interesting dynamics have been reported. In this paper, we consider a prey\u2013predator model with generalist predator subject to Allee effect in predator\u2019s growth rate. In general, a prey\u2013predator system with saturating functional response can be destabilized due to the increase of the carrying capacity of prey which is known as paradox of enrichment. In our model with Allee effect in predator growth, we have shown that increase in carrying capacity of prey helps the populations to survive in a coexistence steady state. The considered model is capable of producing bistable dynamics for a reasonable range of parameter values. The complete dynamics of the system are quite rich and all possible local and global bifurcations are studied to understand the dynamics of the model. Analytical results are verified with numerical examples and successive bifurcations are identified with the help of bifurcation diagrams.<\/jats:p>","DOI":"10.1142\/s0218127420500844","type":"journal-article","created":{"date-parts":[[2020,6,8]],"date-time":"2020-06-08T09:00:08Z","timestamp":1591606808000},"page":"2050084","source":"Crossref","is-referenced-by-count":34,"title":["Rich Bifurcation Structure of Prey\u2013Predator Model Induced by the Allee Effect in the Growth of Generalist Predator"],"prefix":"10.1142","volume":"30","author":[{"given":"Deeptajyoti","family":"Sen","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, IIT Kanpur, Kanpur, U.P., India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sergei","family":"Petrovskii","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Leicester, Leicester \u2013 LE1 7RH, UK"},{"name":"Peoples\u2019 Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St., Moscow 117198, Russian Federation"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"S.","family":"Ghorai","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, IIT Kanpur, Kanpur, U.P., India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4327-5904","authenticated-orcid":false,"given":"Malay","family":"Banerjee","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, IIT Kanpur, Kanpur, U.P., India"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"219","published-online":{"date-parts":[[2020,6,8]]},"reference":[{"key":"S0218127420500844BIB001","doi-asserted-by":"publisher","DOI":"10.1142\/S0218339012500027"},{"key":"S0218127420500844BIB002","doi-asserted-by":"publisher","DOI":"10.1002\/jez.1400610202"},{"key":"S0218127420500844BIB004","doi-asserted-by":"publisher","DOI":"10.1142\/2284"},{"key":"S0218127420500844BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/j.tree.2006.12.002"},{"key":"S0218127420500844BIB006","doi-asserted-by":"publisher","DOI":"10.1007\/s002850000078"},{"key":"S0218127420500844BIB007","doi-asserted-by":"publisher","DOI":"10.1016\/j.crma.2005.09.033"},{"key":"S0218127420500844BIB008","doi-asserted-by":"publisher","DOI":"10.1126\/science.1203672"},{"key":"S0218127420500844BIB009","doi-asserted-by":"publisher","DOI":"10.1007\/BF00275207"},{"key":"S0218127420500844BIB010","doi-asserted-by":"publisher","DOI":"10.1038\/375227a0"},{"key":"S0218127420500844BIB011","doi-asserted-by":"publisher","DOI":"10.1093\/acprof:oso\/9780198570301.001.0001"},{"key":"S0218127420500844BIB012","volume-title":"Chaos in Ecology: Experimental Nonlinear Dynamics","volume":"1","author":"Cushing J. M.","year":"2002"},{"key":"S0218127420500844BIB013","volume-title":"Integrodifferential Equations and Delay Models in Population Dynamics","volume":"20","author":"Cushing J. M.","year":"2013"},{"key":"S0218127420500844BIB014","doi-asserted-by":"publisher","DOI":"10.1046\/j.1461-0248.2001.00223.x"},{"key":"S0218127420500844BIB015","doi-asserted-by":"publisher","DOI":"10.1098\/rsbl.2004.0246"},{"key":"S0218127420500844BIB016","doi-asserted-by":"publisher","DOI":"10.2307\/5465"},{"key":"S0218127420500844BIB017","doi-asserted-by":"publisher","DOI":"10.2307\/1940591"},{"key":"S0218127420500844BIB018","doi-asserted-by":"publisher","DOI":"10.1126\/science.aat6412"},{"key":"S0218127420500844BIB019","doi-asserted-by":"publisher","DOI":"10.1016\/j.ecolmodel.2005.05.001"},{"key":"S0218127420500844BIB020","doi-asserted-by":"publisher","DOI":"10.1007\/s00285-012-0584-z"},{"key":"S0218127420500844BIB021","doi-asserted-by":"publisher","DOI":"10.1890\/07-1505.1"},{"key":"S0218127420500844BIB022","volume-title":"Delay Differential Equations: With Applications in Population Dynamics","volume":"191","author":"Kuang Y.","year":"1993"},{"key":"S0218127420500844BIB023","first-page":"129","volume":"17","author":"Kuang Y.","year":"2002","journal-title":"J. Biomath."},{"key":"S0218127420500844BIB024","doi-asserted-by":"publisher","DOI":"10.1080\/00036811.2010.483557"},{"key":"S0218127420500844BIB025","doi-asserted-by":"publisher","DOI":"10.1016\/j.nonrwa.2010.10.016"},{"key":"S0218127420500844BIB026","doi-asserted-by":"publisher","DOI":"10.2307\/1940365"},{"key":"S0218127420500844BIB027","doi-asserted-by":"publisher","DOI":"10.1038\/261459a0"},{"key":"S0218127420500844BIB028","doi-asserted-by":"publisher","DOI":"10.2307\/1939558"},{"key":"S0218127420500844BIB029","doi-asserted-by":"publisher","DOI":"10.1016\/j.jtbi.2016.02.016"},{"key":"S0218127420500844BIB030","doi-asserted-by":"publisher","DOI":"10.1038\/316628a0"},{"key":"S0218127420500844BIB031","volume-title":"Differential Equations and Dynamical Systems","volume":"7","author":"Perko L.","year":"2013"},{"key":"S0218127420500844BIB032","doi-asserted-by":"publisher","DOI":"10.1016\/j.ecocom.2003.10.001"},{"key":"S0218127420500844BIB033","doi-asserted-by":"publisher","DOI":"10.1126\/science.171.3969.385"},{"key":"S0218127420500844BIB034","doi-asserted-by":"publisher","DOI":"10.1051\/mmnp\/20094207"},{"key":"S0218127420500844BIB035","doi-asserted-by":"crossref","DOI":"10.1515\/9781400833276","volume-title":"Critical Transitions in Nature and Society","volume":"16","author":"Scheffer M.","year":"2009"},{"key":"S0218127420500844BIB036","doi-asserted-by":"publisher","DOI":"10.1038\/nature08227"},{"key":"S0218127420500844BIB037","doi-asserted-by":"publisher","DOI":"10.1016\/j.ecocom.2012.01.002"},{"key":"S0218127420500844BIB038","doi-asserted-by":"publisher","DOI":"10.1007\/BF00277664"},{"key":"S0218127420500844BIB039","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0010761"},{"key":"S0218127420500844BIB040","doi-asserted-by":"publisher","DOI":"10.1142\/2942"},{"key":"S0218127420500844BIB041","doi-asserted-by":"publisher","DOI":"10.1007\/s00285-015-0856-5"},{"key":"S0218127420500844BIB042","volume-title":"Complex Population Dynamics: A Theoretical\/Empirical Synthesis","volume":"35","author":"Turchin P.","year":"2003"},{"key":"S0218127420500844BIB043","doi-asserted-by":"publisher","DOI":"10.1016\/j.mbs.2007.02.006"},{"key":"S0218127420500844BIB044","doi-asserted-by":"publisher","DOI":"10.1007\/s00285-010-0332-1"},{"key":"S0218127420500844BIB045","doi-asserted-by":"publisher","DOI":"10.1051\/mmnp\/20138307"},{"key":"S0218127420500844BIB046","doi-asserted-by":"publisher","DOI":"10.1016\/j.nonrwa.2006.06.006"},{"key":"S0218127420500844BIB047","doi-asserted-by":"publisher","DOI":"10.1016\/j.nonrwa.2007.05.004"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127420500844","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,3,19]],"date-time":"2021-03-19T05:23:22Z","timestamp":1616131402000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127420500844"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,5]]},"references-count":46,"journal-issue":{"issue":"06","published-print":{"date-parts":[[2020,5]]}},"alternative-id":["10.1142\/S0218127420500844"],"URL":"https:\/\/doi.org\/10.1142\/s0218127420500844","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,5]]}}}