AdvancesinAppliedMathematicsA^êÆ?Ð,2023,12(8),3709-3727PublishedOnlineAugust2023inHans.https://www.hanspub.org/journal/aamhttps://doi.org/10.12677/aam.2023.128366‘kÜŠÓ�HollingIII.�Óö-��.ªªªëëëɲ“‰ŒÆêÆÆ�§úôɲÂvFϵ2023c7�26F¶¹^Fϵ2023c8�18F¶uÙFϵ2023c8�24FÁ‡�©ïÄ�‘krfAllee�A§ÜŠÓ�Ú‡Ó1•�Óö-��.�ÄåÆ1•"·‚?1�•[�²ï:•35Ú-½5©Û,©Û�Q(©|§Hopf©|Ú{‘�4•‚�k:§¿ÏLêŠ�[5�ynØ(J§��4•‚�{‘�k:�•35§?���XÚ–�•3n‡�•�4•‚§L²3ÜŠÓ��K•e§äkAllee�AÚ‡Ó1•�Óö-��.�ÄåÆ1•¬•\E,"'…cÜŠÓ�§Allee�A§Hopf©|§Óö-��.§Q(©|§{‘�4•‚�k:APredator-PreyModelofCollaborativeHuntingwithHollingIIITypeTaoWenSchoolofMathematics,HangzhouNormalUniversity,HangzhouZhejiangReceived:Jul.26th,2023;accepted:Aug.18th,2023;published:Aug.24th,2023©ÙÚ^:ªë.‘kÜŠÓ�HollingIII.�Óö-��.[J].A^êÆ?Ð,2023,12(8):3709-3727.DOI:10.12677/aam.2023.128366ªëAbstractThispaperinvestigatesthedynamicbehaviorofapredator-preymodelwithstrongandweakAlleeeffects,cooperativehunting,andanti-predatorbehavior.Wediscusstheexistenceandstabilityoftheequilibriumpoints,andweperformadetailedbifurcationanalysisincludingthesaddle-nodebifurcation,Hopfbifurcationandcodimension-2cuspoflimitcycle,thenweverifiedthetheoreticalresultsthroughnumericalsimula-tion,obtainedtheexistenceofthecodimension-2cuspoftheLimitcycle,andthenobtainedthatthesystemhasatleastthreecoexistingLimitcycles,indicatingthatundertheinfluenceofcooperativehunting,thedynamicbehaviorofthepredator-preymodelwithAlleeeffectandanti-predatorbehaviorwillbemorecomplex.KeywordsCooperativeHunting,AlleeEffect,HopfBifurcation,Predator-PreyModel,Saddle-NodeBifurcation,Codimension-2CuspofLimitCycleCopyrightc⃝2023byauthor(s)andHansPublishersInc.ThisworkislicensedundertheCreativeCommonsAttributionInternationalLicense(CCBY4.0).http://creativecommons.org/licenses/by/4.0/1.0�É©zYaoetal.[1]éuÜŠÓ�ïÄ�éu,·‚ïá±e‘kAllee�AÚ‡Ó...
