{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,24]],"date-time":"2026-06-24T06:38:10Z","timestamp":1782283090595,"version":"3.54.5"},"reference-count":22,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","funder":[{"name":"NSFC grants","award":["11471133"],"award-info":[{"award-number":["11471133"]}]},{"name":"self-determined research funds of CCNU from the colleges' basic research and operation of MOE","award":["CCNU14A02003"],"award-info":[{"award-number":["CCNU14A02003"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2016,2]]},"abstract":"<jats:p> It was shown in [Li &amp; Xiao, 2007] that in a predator\u2013prey model of Leslie type with simplified Holling type IV functional response some complex bifurcations can occur simultaneously for some values of parameters, such as codimension 1 subcritical Hopf bifurcation and codimension 2 Bogdanov\u2013Takens bifurcation. In this paper, we show that for the same model there exists a unique degenerate positive equilibrium which is a degenerate Bogdanov\u2013Takens singularity (focus case) of codimension 3 for other values of parameters. We prove that the model exhibits degenerate focus type Bogdanov\u2013Takens bifurcation of codimension 3 around the unique degenerate positive equilibrium. Numerical simulations, including the coexistence of three hyperbolic positive equilibria, two limit cycles, bistability states (one stable equilibrium and one stable limit cycle, or two stable equilibria), tristability states (two stable equilibria and one stable limit cycle), a stable limit cycle enclosing a homoclinic loop, a homoclinic loop enclosing an unstable limit cycle, or a stable limit cycle enclosing three unstable hyperbolic positive equilibria for various parameter values, confirm the theoretical results. <\/jats:p>","DOI":"10.1142\/s0218127416500346","type":"journal-article","created":{"date-parts":[[2016,3,9]],"date-time":"2016-03-09T22:26:20Z","timestamp":1457562380000},"page":"1650034","source":"Crossref","is-referenced-by-count":59,"title":["Bifurcation of Codimension 3 in a Predator\u2013Prey System of Leslie Type with Simplified Holling Type IV Functional Response"],"prefix":"10.1142","volume":"26","author":[{"given":"Jicai","family":"Huang","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Central China Normal University, Wuhan, Hubei 430079, P. R. China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaojing","family":"Xia","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Central China Normal University, Wuhan, Hubei 430079, P. R. China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xinan","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Central China Normal University, Wuhan, Hubei 430079, P. R. China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shigui","family":"Ruan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Miami, Coral Gables, FL 33124-4250, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"219","published-online":{"date-parts":[[2016,3,9]]},"reference":[{"key":"S0218127416500346BIB001","doi-asserted-by":"publisher","DOI":"10.1137\/050627757"},{"key":"S0218127416500346BIB002","doi-asserted-by":"publisher","DOI":"10.1007\/s00285-012-0546-5"},{"key":"S0218127416500346BIB003","first-page":"94","volume-title":"Theoretical Ecology: Principles and Applications","author":"Caughley G.","year":"1976"},{"key":"S0218127416500346BIB004","doi-asserted-by":"publisher","DOI":"10.1137\/120895858"},{"key":"S0218127416500346BIB005","doi-asserted-by":"publisher","DOI":"10.1007\/s002850050095"},{"key":"S0218127416500346BIB006","series-title":"Lecture Notes in Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/BFb0098353","volume-title":"Bifurcation of Planar Vector Fields, Nilpotent Singularities and Abelian Integrals","volume":"1480","author":"Dumortier F.","year":"1991"},{"key":"S0218127416500346BIB007","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2010.06.021"},{"key":"S0218127416500346BIB008","doi-asserted-by":"publisher","DOI":"10.3934\/dcdsb.2011.15.93"},{"key":"S0218127416500346BIB009","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127413501642"},{"key":"S0218127416500346BIB010","doi-asserted-by":"publisher","DOI":"10.3934\/dcdsb.2013.18.2101"},{"key":"S0218127416500346BIB011","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2014.04.024"},{"key":"S0218127416500346BIB012","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2006.03.068"},{"key":"S0218127416500346BIB013","volume-title":"Stability and Complexity in Model Ecosystems","author":"May R. 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