{"id":"https://openalex.org/W2177112675","doi":"https://doi.org/10.1142/s0218127415400143","title":"Bifurcation and Stability in a Delayed Predator\u2013Prey Model with Mixed Functional Responses","display_name":"Bifurcation and Stability in a Delayed Predator\u2013Prey Model with Mixed Functional Responses","publication_year":2015,"publication_date":"2015-06-30","ids":{"openalex":"https://openalex.org/W2177112675","doi":"https://doi.org/10.1142/s0218127415400143","mag":"2177112675"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127415400143","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127415400143","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5016073934","display_name":"Radouane Yafia","orcid":"https://orcid.org/0000-0002-9824-9036"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"R. Yafia","raw_affiliation_strings":["Ibn Zohr University, Polydisciplinary Faculty of Ouarzazate, B.P. 638, Ouarzazate, Morocco"],"affiliations":[{"raw_affiliation_string":"Ibn Zohr University, Polydisciplinary Faculty of Ouarzazate, B.P. 638, Ouarzazate, Morocco","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036156842","display_name":"M. A. Aziz-Alaoui","orcid":"https://orcid.org/0000-0001-5198-4597"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I141576021","display_name":"Universit\u00e9 Le Havre Normandie","ror":"https://ror.org/05v509s40","country_code":"FR","type":"education","lineage":["https://openalex.org/I141576021","https://openalex.org/I4210105918"]},{"id":"https://openalex.org/I4210105918","display_name":"Normandie Universit\u00e9","ror":"https://ror.org/01k40cz91","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210105918"]},{"id":"https://openalex.org/I4392021130","display_name":"Laboratoire de Math\u00e9matiques Appliqu\u00e9es du Havre","ror":"https://ror.org/017vnhv07","country_code":"FR","type":"facility","lineage":["https://openalex.org/I141576021","https://openalex.org/I4210105918","https://openalex.org/I4392021130"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"M. A. Aziz-Alaoui","raw_affiliation_strings":["Normandie University, France","ULH, LMAH, F-76600 Le Havre, FR CNRS 3335, ISCN, 25 rue Philippe Lebon, 76600 Le Havre, France"],"affiliations":[{"raw_affiliation_string":"Normandie University, France","institution_ids":["https://openalex.org/I4210105918"]},{"raw_affiliation_string":"ULH, LMAH, F-76600 Le Havre, FR CNRS 3335, ISCN, 25 rue Philippe Lebon, 76600 Le Havre, France","institution_ids":["https://openalex.org/I4392021130","https://openalex.org/I141576021","https://openalex.org/I1294671590"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005319900","display_name":"H. Merdan","orcid":"https://orcid.org/0000-0003-2311-5348"},"institutions":[{"id":"https://openalex.org/I13236232","display_name":"TOBB University of Economics and Technology","ror":"https://ror.org/03ewx7v96","country_code":"TR","type":"education","lineage":["https://openalex.org/I13236232"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"H. Merdan","raw_affiliation_strings":["Department of Mathematics, TOBB University of Economics and Technology, S\u00f6g\u00fct\u00f6z\u00fc Cad. No. 43 06530, S\u00f6g\u00fct\u00f6z\u00fc, Ankara, Turkey"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, TOBB University of Economics and Technology, S\u00f6g\u00fct\u00f6z\u00fc Cad. No. 43 06530, S\u00f6g\u00fct\u00f6z\u00fc, Ankara, Turkey","institution_ids":["https://openalex.org/I13236232"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5051057617","display_name":"Jean Jules Tewa","orcid":"https://orcid.org/0000-0002-4700-3650"},"institutions":[{"id":"https://openalex.org/I4210153851","display_name":"Unit\u00e9 de Mod\u00e9lisation Math\u00e9matique et Informatique des Syst\u00e8mes Complexes","ror":"https://ror.org/053kxkj53","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1327553481","https://openalex.org/I154202486","https://openalex.org/I2799535048","https://openalex.org/I2802818602","https://openalex.org/I39804081","https://openalex.org/I4210088668","https://openalex.org/I4210090127","https://openalex.org/I4210113730","https://openalex.org/I4210131494","https://openalex.org/I4210153851","https://openalex.org/I4210166444","https://openalex.org/I4405257220"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"J. J. Tewa","raw_affiliation_strings":["UMI 209 UMMISCO, GRIMCAPE, Yaounde, Cameroon"],"affiliations":[{"raw_affiliation_string":"UMI 209 UMMISCO, GRIMCAPE, Yaounde, Cameroon","institution_ids":["https://openalex.org/I4210153851"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5016073934"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.1032555,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"25","issue":"07","first_page":"1540014","last_page":"1540014"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},"topics":[{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T11764","display_name":"Evolution and Genetic Dynamics","score":0.9965000152587891,"subfield":{"id":"https://openalex.org/subfields/1311","display_name":"Genetics"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9891999959945679,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/hopf-bifurcation","display_name":"Hopf bifurcation","score":0.8119366765022278},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6976988315582275},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.6247899532318115},{"id":"https://openalex.org/keywords/functional-response","display_name":"Functional response","score":0.5807433724403381},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.565297544002533},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5143333673477173},{"id":"https://openalex.org/keywords/saddle-node-bifurcation","display_name":"Saddle-node bifurcation","score":0.49945735931396484},{"id":"https://openalex.org/keywords/predation","display_name":"Predation","score":0.4907878339290619},{"id":"https://openalex.org/keywords/bifurcation-diagram","display_name":"Bifurcation diagram","score":0.466442346572876},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4529142379760742},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.44915643334388733},{"id":"https://openalex.org/keywords/biological-applications-of-bifurcation-theory","display_name":"Biological applications of bifurcation theory","score":0.43459299206733704},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.3654560446739197},{"id":"https://openalex.org/keywords/predator","display_name":"Predator","score":0.33303767442703247},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.1452067494392395},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14066249132156372},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11943447589874268},{"id":"https://openalex.org/keywords/ecology","display_name":"Ecology","score":0.08017656207084656},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.0542415976524353}],"concepts":[{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.8119366765022278},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6976988315582275},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.6247899532318115},{"id":"https://openalex.org/C110201527","wikidata":"https://www.wikidata.org/wiki/Q5508845","display_name":"Functional response","level":4,"score":0.5807433724403381},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.565297544002533},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5143333673477173},{"id":"https://openalex.org/C101225446","wikidata":"https://www.wikidata.org/wiki/Q740190","display_name":"Saddle-node bifurcation","level":4,"score":0.49945735931396484},{"id":"https://openalex.org/C188382862","wikidata":"https://www.wikidata.org/wiki/Q170430","display_name":"Predation","level":2,"score":0.4907878339290619},{"id":"https://openalex.org/C86243350","wikidata":"https://www.wikidata.org/wiki/Q2595915","display_name":"Bifurcation diagram","level":4,"score":0.466442346572876},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4529142379760742},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.44915643334388733},{"id":"https://openalex.org/C174914120","wikidata":"https://www.wikidata.org/wiki/Q4914973","display_name":"Biological applications of bifurcation theory","level":5,"score":0.43459299206733704},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.3654560446739197},{"id":"https://openalex.org/C96857902","wikidata":"https://www.wikidata.org/wiki/Q2138108","display_name":"Predator","level":3,"score":0.33303767442703247},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.1452067494392395},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14066249132156372},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11943447589874268},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.08017656207084656},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0542415976524353},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218127415400143","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127415400143","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-02304512v1","is_oa":false,"landing_page_url":"https://hal.science/hal-02304512","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International journal of bifurcation and chaos in applied sciences and engineering , 2015, 25 (07), pp.1540014. ⟨10.1142/S0218127415400143⟩","raw_type":"Journal articles"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Life below water","score":0.5299999713897705,"id":"https://metadata.un.org/sdg/14"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1586658033","https://openalex.org/W1965100078","https://openalex.org/W1965549084","https://openalex.org/W2030453979","https://openalex.org/W2040712046","https://openalex.org/W2062210472","https://openalex.org/W2079871064","https://openalex.org/W2081827062","https://openalex.org/W2082582374","https://openalex.org/W2094032066","https://openalex.org/W2129992593","https://openalex.org/W4294576619"],"related_works":["https://openalex.org/W2546487931","https://openalex.org/W3113797113","https://openalex.org/W3210862581","https://openalex.org/W56905705","https://openalex.org/W3123209508","https://openalex.org/W2543553286","https://openalex.org/W2957281485","https://openalex.org/W4379507489","https://openalex.org/W1584629339","https://openalex.org/W2342467592"],"abstract_inverted_index":{"The":[0],"model":[1,10,41,63],"analyzed":[2],"in":[3,84],"this":[4,58],"paper":[5],"is":[6,111],"based":[7],"on":[8],"the":[9,33,36,47,62,93,101,105,108,114],"set":[11],"forth":[12],"by":[13],"Aziz":[14],"Alaoui":[15,19],"et":[16,25],"al.":[17],"[Aziz":[18],"&":[20],"Daher":[21],"Okiye,":[22],"2003;":[23],"Nindjin":[24],"al.,":[26],"2006]":[27],"with":[28,64],"time":[29],"delay,":[30],"which":[31,77],"describes":[32],"competition":[34],"between":[35],"predator":[37],"and":[38,74,88,91],"prey.":[39],"This":[40],"incorporates":[42],"a":[43,69,118],"modified":[44],"version":[45],"of":[46,55,68,86,92,95,107,120],"Leslie\u2013Gower":[48],"functional":[49],"response":[50],"as":[51,53,113,117],"well":[52],"that":[54,122],"Beddington\u2013DeAngelis.":[56],"In":[57],"paper,":[59],"we":[60],"consider":[61],"one":[65],"delay":[66,115],"consisting":[67],"unique":[70],"nontrivial":[71],"equilibrium":[72],"E*":[73],"three":[75],"others":[76],"are":[78,82],"trivial.":[79],"Their":[80],"dynamics":[81],"studied":[83],"terms":[85],"local":[87],"global":[89],"stabilities":[90],"description":[94],"Hopf":[96,109],"bifurcation":[97,110],"at":[98],"E*.":[99],"At":[100],"third":[102],"trivial":[103],"equilibrium,":[104],"existence":[106],"proven":[112],"(taken":[116],"parameter":[119],"bifurcation)":[121],"crosses":[123],"some":[124],"critical":[125],"values.":[126]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-03-24T08:02:53.985720","created_date":"2025-10-10T00:00:00"}