{"id":"https://openalex.org/W2470287079","doi":"https://doi.org/10.1142/s021812741650108x","title":"Big Bang Bifurcation Analysis and Allee Effect in Generic Growth Functions","display_name":"Big Bang Bifurcation Analysis and Allee Effect in Generic Growth Functions","publication_year":2016,"publication_date":"2016-06-15","ids":{"openalex":"https://openalex.org/W2470287079","doi":"https://doi.org/10.1142/s021812741650108x","mag":"2470287079"},"language":"en","primary_location":{"id":"doi:10.1142/s021812741650108x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021812741650108x","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/A5057211137","display_name":"J. Leonel Rocha","orcid":"https://orcid.org/0000-0001-8053-6822"},"institutions":[{"id":"https://openalex.org/I203847022","display_name":"Instituto Polit\u00e9cnico de Lisboa","ror":"https://ror.org/04ea70f07","country_code":"PT","type":"education","lineage":["https://openalex.org/I203847022"]}],"countries":["PT"],"is_corresponding":true,"raw_author_name":"J. Leonel Rocha","raw_affiliation_strings":["ADM, ISEL-Instituto Sup. de Engenharia de Lisboa, Instituto Polit\u00e9cnico de Lisboa, Rua Conselheiro Em\u00eddio Navarro 1, 1959-007 Lisboa, Portugal"],"affiliations":[{"raw_affiliation_string":"ADM, ISEL-Instituto Sup. de Engenharia de Lisboa, Instituto Polit\u00e9cnico de Lisboa, Rua Conselheiro Em\u00eddio Navarro 1, 1959-007 Lisboa, Portugal","institution_ids":["https://openalex.org/I203847022"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108406533","display_name":"Abdel-Kaddous Taha","orcid":"https://orcid.org/0000-0002-6468-3803"},"institutions":[{"id":"https://openalex.org/I196454796","display_name":"Institut National des Sciences Appliqu\u00e9es de Toulouse","ror":"https://ror.org/01h8pf755","country_code":"FR","type":"education","lineage":["https://openalex.org/I196454796","https://openalex.org/I4405258862"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Abdel-Kaddous Taha","raw_affiliation_strings":["INSA, University of Toulouse, 135 Avenue de Rangueil, 31077 Toulouse, France"],"affiliations":[{"raw_affiliation_string":"INSA, University of Toulouse, 135 Avenue de Rangueil, 31077 Toulouse, France","institution_ids":["https://openalex.org/I196454796"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5031427355","display_name":"Dani\u00e8le Fournier-Prunaret","orcid":"https://orcid.org/0000-0003-0036-8932"},"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/I190497903","display_name":"Laboratoire d'Analyse et d'Architecture des Syst\u00e8mes","ror":"https://ror.org/03vcm6439","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I134560555","https://openalex.org/I190497903","https://openalex.org/I196454796","https://openalex.org/I205747304","https://openalex.org/I205747304","https://openalex.org/I4210095849","https://openalex.org/I4210159245","https://openalex.org/I4387153255","https://openalex.org/I4405258862","https://openalex.org/I4405258862","https://openalex.org/I4405258862","https://openalex.org/I4405258862"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"D. Fournier-Prunaret","raw_affiliation_strings":["LAAS-CNRS, INSA, University of Toulouse, 7 Avenue du Colonel Roche, 31077 Toulouse, France"],"affiliations":[{"raw_affiliation_string":"LAAS-CNRS, INSA, University of Toulouse, 7 Avenue du Colonel Roche, 31077 Toulouse, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I190497903"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5057211137"],"corresponding_institution_ids":["https://openalex.org/I203847022"],"apc_list":null,"apc_paid":null,"fwci":0.5746,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.76410118,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"26","issue":"06","first_page":"1650108","last_page":"1650108"},"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":0.9854999780654907,"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":0.9854999780654907,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.984499990940094,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.9830999970436096,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/allee-effect","display_name":"Allee effect","score":0.9645740985870361},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7122808694839478},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.6996487379074097},{"id":"https://openalex.org/keywords/saddle-node-bifurcation","display_name":"Saddle-node bifurcation","score":0.5315898060798645},{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.5082340240478516},{"id":"https://openalex.org/keywords/transcritical-bifurcation","display_name":"Transcritical bifurcation","score":0.5074178576469421},{"id":"https://openalex.org/keywords/bogdanov\u2013takens-bifurcation","display_name":"Bogdanov\u2013Takens bifurcation","score":0.48129549622535706},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.4774666130542755},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.47153928875923157},{"id":"https://openalex.org/keywords/biological-applications-of-bifurcation-theory","display_name":"Biological applications of bifurcation theory","score":0.4571826457977295},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.3859897255897522},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.36929112672805786},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.16272768378257751},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1132485568523407}],"concepts":[{"id":"https://openalex.org/C10958125","wikidata":"https://www.wikidata.org/wiki/Q2301505","display_name":"Allee effect","level":3,"score":0.9645740985870361},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7122808694839478},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.6996487379074097},{"id":"https://openalex.org/C101225446","wikidata":"https://www.wikidata.org/wiki/Q740190","display_name":"Saddle-node bifurcation","level":4,"score":0.5315898060798645},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.5082340240478516},{"id":"https://openalex.org/C55610538","wikidata":"https://www.wikidata.org/wiki/Q1502581","display_name":"Transcritical bifurcation","level":5,"score":0.5074178576469421},{"id":"https://openalex.org/C22257346","wikidata":"https://www.wikidata.org/wiki/Q4937510","display_name":"Bogdanov\u2013Takens bifurcation","level":5,"score":0.48129549622535706},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4774666130542755},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47153928875923157},{"id":"https://openalex.org/C174914120","wikidata":"https://www.wikidata.org/wiki/Q4914973","display_name":"Biological applications of bifurcation theory","level":5,"score":0.4571826457977295},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.3859897255897522},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.36929112672805786},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.16272768378257751},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1132485568523407},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.0},{"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/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s021812741650108x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021812741650108x","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-01760758v1","is_oa":false,"landing_page_url":"https://laas.hal.science/hal-01760758","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 , 2016, 26 (06), &#x27E8;10.1142/S021812741650108X&#x27E9;","raw_type":"Journal articles"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320334779","display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","ror":"https://ror.org/00snfqn58"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W207809827","https://openalex.org/W1973081537","https://openalex.org/W1973988557","https://openalex.org/W2004840651","https://openalex.org/W2009276987","https://openalex.org/W2022969957","https://openalex.org/W2032479971","https://openalex.org/W2033102981","https://openalex.org/W2043508446","https://openalex.org/W2046557303","https://openalex.org/W2049203971","https://openalex.org/W2055502660","https://openalex.org/W2076972098","https://openalex.org/W2095379271","https://openalex.org/W2107487258","https://openalex.org/W2117974455","https://openalex.org/W2137405498","https://openalex.org/W2148180014","https://openalex.org/W2157833053","https://openalex.org/W2168432867","https://openalex.org/W2174392345","https://openalex.org/W2321390672","https://openalex.org/W2322825892","https://openalex.org/W2386261390","https://openalex.org/W2499095841","https://openalex.org/W2519692328","https://openalex.org/W2639639281","https://openalex.org/W4232709242","https://openalex.org/W4250146611","https://openalex.org/W4292510609"],"related_works":["https://openalex.org/W2356715721","https://openalex.org/W2546487931","https://openalex.org/W2025138898","https://openalex.org/W4388961837","https://openalex.org/W152938242","https://openalex.org/W3040509139","https://openalex.org/W2087757984","https://openalex.org/W2325048728","https://openalex.org/W4365441268","https://openalex.org/W2356226573"],"abstract_inverted_index":{"The":[0,49,76,89],"main":[1],"purpose":[2],"of":[3,14,26,33,41,51,54,62,84,103,127,142,158],"this":[4,52],"work":[5],"is":[6,79,92],"to":[7,58,118,151],"study":[8],"the":[9,22,27,46,67,82,99,104,110,131,140,153],"dynamics":[10],"and":[11,43,65,72,86],"bifurcation":[12,74,77,97,115,122,156],"properties":[13],"generic":[15,28],"growth":[16,29],"functions,":[17],"which":[18],"are":[19,137],"defined":[20],"by":[21],"population":[23],"size":[24],"functions":[25,64],"equation.":[30],"This":[31],"family":[32],"unimodal":[34],"maps":[35],"naturally":[36],"incorporates":[37],"a":[38,60],"principal":[39],"focus":[40],"ecological":[42],"biological":[44],"research:":[45],"Allee":[47],"effect.":[48],"analysis":[50,78,157],"kind":[53],"extinction":[55],"phenomenon":[56],"allows":[57],"identify":[59],"class":[61],"Allee\u2019s":[63,69,73],"characterize":[66],"corresponding":[68,132],"effect":[70],"region":[71],"curve.":[75],"founded":[80],"on":[81],"performance":[83],"fold":[85],"flip":[87],"bifurcations.":[88],"dynamical":[90],"behavior":[91],"rich":[93],"with":[94,124],"abundant":[95],"complex":[96],"structures,":[98],"big":[100,120,154],"bang":[101,121,155],"bifurcations":[102],"so-called":[105],"\u201cbox-within-a-box\u201d":[106],"fractal":[107],"type":[108],"being":[109],"most":[111],"outstanding.":[112],"Moreover,":[113],"these":[114,145],"cascades":[116],"converge":[117],"different":[119],"curves":[123],"distinct":[125],"kinds":[126],"boxes,":[128],"where":[129],"for":[130],"parameter":[133],"values":[134],"several":[135],"attractors":[136],"associated.":[138],"To":[139],"best":[141],"our":[143],"knowledge,":[144],"results":[146],"represent":[147],"an":[148],"original":[149],"contribution":[150],"clarify":[152],"continuous":[159],"1D":[160],"maps.":[161]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2016-07-22T00:00:00"}
