{"id":"https://openalex.org/W2535820282","doi":"https://doi.org/10.1080/00207721.2016.1244308","title":"Global stability and Neimark-Sacker bifurcation of a host-parasitoid model","display_name":"Global stability and Neimark-Sacker bifurcation of a host-parasitoid model","publication_year":2016,"publication_date":"2016-10-21","ids":{"openalex":"https://openalex.org/W2535820282","doi":"https://doi.org/10.1080/00207721.2016.1244308","mag":"2535820282"},"language":"en","primary_location":{"id":"doi:10.1080/00207721.2016.1244308","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207721.2016.1244308","pdf_url":null,"source":{"id":"https://openalex.org/S129640837","display_name":"International Journal of Systems Science","issn_l":"0020-7721","issn":["0020-7721","1464-5319"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Systems Science","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/A5024827048","display_name":"Qamar Din","orcid":"https://orcid.org/0000-0002-0999-7404"},"institutions":[{"id":"https://openalex.org/I4387154749","display_name":"University of Poonch Rawalakot","ror":"https://ror.org/045arbm30","country_code":null,"type":"education","lineage":["https://openalex.org/I4387154749"]}],"countries":["PK"],"is_corresponding":true,"raw_author_name":"Qamar Din","raw_affiliation_strings":["Department of Mathematics, The University of Poonch Rawalakot, Rawalakot, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, The University of Poonch Rawalakot, Rawalakot, Pakistan","institution_ids":["https://openalex.org/I4387154749"]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5024827048"],"corresponding_institution_ids":["https://openalex.org/I4387154749"],"apc_list":null,"apc_paid":null,"fwci":4.7031,"has_fulltext":false,"cited_by_count":38,"citation_normalized_percentile":{"value":0.95346116,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"48","issue":"6","first_page":"1194","last_page":"1202"},"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.992900013923645,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.991599977016449,"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/mathematics","display_name":"Mathematics","score":0.7619200944900513},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.6744476556777954},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.6530733108520508},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5740296244621277},{"id":"https://openalex.org/keywords/bifurcation-diagram","display_name":"Bifurcation diagram","score":0.5673257112503052},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.557064414024353},{"id":"https://openalex.org/keywords/lyapunov-exponent","display_name":"Lyapunov exponent","score":0.5231351256370544},{"id":"https://openalex.org/keywords/bifurcation-theory","display_name":"Bifurcation theory","score":0.5060176253318787},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.46736499667167664},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.44893205165863037},{"id":"https://openalex.org/keywords/equilibrium-point","display_name":"Equilibrium point","score":0.4463561475276947},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.4331989586353302},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.41286739706993103},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.4079012870788574},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.34458085894584656},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.34120768308639526},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.30788230895996094},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1417035460472107},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.11890175938606262},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.11333322525024414},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0801524817943573}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7619200944900513},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.6744476556777954},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.6530733108520508},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5740296244621277},{"id":"https://openalex.org/C86243350","wikidata":"https://www.wikidata.org/wiki/Q2595915","display_name":"Bifurcation diagram","level":4,"score":0.5673257112503052},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.557064414024353},{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.5231351256370544},{"id":"https://openalex.org/C85075877","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Bifurcation theory","level":4,"score":0.5060176253318787},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.46736499667167664},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.44893205165863037},{"id":"https://openalex.org/C94766913","wikidata":"https://www.wikidata.org/wiki/Q1530271","display_name":"Equilibrium point","level":3,"score":0.4463561475276947},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.4331989586353302},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.41286739706993103},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4079012870788574},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34458085894584656},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.34120768308639526},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.30788230895996094},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1417035460472107},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.11890175938606262},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.11333322525024414},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0801524817943573},{"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/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","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},{"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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/00207721.2016.1244308","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207721.2016.1244308","pdf_url":null,"source":{"id":"https://openalex.org/S129640837","display_name":"International Journal of Systems Science","issn_l":"0020-7721","issn":["0020-7721","1464-5319"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Systems Science","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:taf:tsysxx:v:48:y:2017:i:6:p:1194-1202","is_oa":false,"landing_page_url":"http://hdl.handle.net/10.1080/00207721.2016.1244308","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W13811575","https://openalex.org/W370471672","https://openalex.org/W589092635","https://openalex.org/W1510531757","https://openalex.org/W1549251788","https://openalex.org/W1588340316","https://openalex.org/W1969672820","https://openalex.org/W1972487182","https://openalex.org/W2002944058","https://openalex.org/W2008670106","https://openalex.org/W2015333868","https://openalex.org/W2025904721","https://openalex.org/W2028688331","https://openalex.org/W2060891188","https://openalex.org/W2062563514","https://openalex.org/W2065705412","https://openalex.org/W2066994392","https://openalex.org/W2072583653","https://openalex.org/W2087669172","https://openalex.org/W2193865653","https://openalex.org/W2316904041","https://openalex.org/W2321919917","https://openalex.org/W2490508364","https://openalex.org/W2565873252","https://openalex.org/W4255777804","https://openalex.org/W4300473623"],"related_works":["https://openalex.org/W2404180431","https://openalex.org/W2364686153","https://openalex.org/W2072163537","https://openalex.org/W1989697011","https://openalex.org/W2803928976","https://openalex.org/W2033303058","https://openalex.org/W4382882835","https://openalex.org/W1583685166","https://openalex.org/W37064175","https://openalex.org/W2083922599"],"abstract_inverted_index":{"We":[0],"investigate":[1],"qualitative":[2],"behaviour":[3,75,94],"of":[4,14,19,27,35,37,55,69,80,84,92],"a":[5,77],"density-dependent":[6],"discrete-time":[7],"host-parasitoid":[8,39],"model.":[9,40,97],"Particularly,":[10],"we":[11],"study":[12],"boundedness":[13],"solutions,":[15],"existence":[16],"and":[17,23,33],"uniqueness":[18],"positive":[20,30],"steady-state,":[21],"local":[22],"global":[24],"asymptotic":[25],"stability":[26],"the":[28,47,53,85,90,96],"unique":[29],"equilibrium":[31],"point":[32],"rate":[34],"convergence":[36],"modified":[38],"Moreover,":[41],"it":[42],"is":[43],"also":[44],"proved":[45],"that":[46],"system":[48],"undergoes":[49],"Neimark-Sacker":[50],"bifurcation":[51,56],"with":[52],"help":[54],"theory.":[57],"Finally,":[58],"numerical":[59,70],"simulations":[60,71],"are":[61],"provided":[62],"to":[63],"illustrate":[64],"theoretical":[65],"results.":[66],"These":[67],"results":[68],"demonstrate":[72],"chaotic":[73,93],"long-term":[74],"over":[76],"broad":[78],"range":[79],"parameters.":[81],"The":[82],"computation":[83],"maximum":[86],"Lyapunov":[87],"exponents":[88],"confirm":[89],"presence":[91],"in":[95]},"counts_by_year":[{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":7}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}
