{"id":"https://openalex.org/W4416447451","doi":"https://doi.org/10.1155/jama/9030706","title":"Dynamics of Allee and Refuge Effects in Prey\u2013Predator System With Holling\u2032s Type III Functional Response","display_name":"Dynamics of Allee and Refuge Effects in Prey\u2013Predator System With Holling\u2032s Type III Functional Response","publication_year":2025,"publication_date":"2025-01-01","ids":{"openalex":"https://openalex.org/W4416447451","doi":"https://doi.org/10.1155/jama/9030706"},"language":"en","primary_location":{"id":"doi:10.1155/jama/9030706","is_oa":true,"landing_page_url":"https://doi.org/10.1155/jama/9030706","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1155/jama/9030706","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1155/jama/9030706","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036161481","display_name":"Mussa A. Stephano","orcid":"https://orcid.org/0000-0003-2070-3443"},"institutions":[{"id":"https://openalex.org/I182078086","display_name":"University of Dar es Salaam","ror":"https://ror.org/0479aed98","country_code":"TZ","type":"education","lineage":["https://openalex.org/I182078086"]}],"countries":["TZ"],"is_corresponding":true,"raw_author_name":"Mussa A. Stephano","raw_affiliation_strings":["Department of Mathematics ,  Physics and Informatics ,  Mkwawa University College of Education ,  University of Dar es Salaam ,  Iringa ,  Tanzania , muce.ac.tz"],"raw_orcid":"https://orcid.org/0000-0003-2070-3443","affiliations":[{"raw_affiliation_string":"Department of Mathematics ,  Physics and Informatics ,  Mkwawa University College of Education ,  University of Dar es Salaam ,  Iringa ,  Tanzania , muce.ac.tz","institution_ids":["https://openalex.org/I182078086"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5036161481"],"corresponding_institution_ids":["https://openalex.org/I182078086"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.41477642,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"2025","issue":"1","first_page":null,"last_page":null},"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":0.9628999829292297,"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":0.9628999829292297,"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/T13187","display_name":"Diffusion and Search Dynamics","score":0.007300000172108412,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"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/T11252","display_name":"Evolutionary Game Theory and Cooperation","score":0.006500000134110451,"subfield":{"id":"https://openalex.org/subfields/3312","display_name":"Sociology and Political Science"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/allee-effect","display_name":"Allee effect","score":0.9941999912261963},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.6333000063896179},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.4997999966144562},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.44200000166893005},{"id":"https://openalex.org/keywords/dynamics","display_name":"Dynamics (music)","score":0.3903000056743622},{"id":"https://openalex.org/keywords/predation","display_name":"Predation","score":0.3578000068664551},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.35659998655319214}],"concepts":[{"id":"https://openalex.org/C10958125","wikidata":"https://www.wikidata.org/wiki/Q2301505","display_name":"Allee effect","level":3,"score":0.9941999912261963},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.6333000063896179},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5112000107765198},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5015000104904175},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.4997999966144562},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.44200000166893005},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4049000144004822},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.3903000056743622},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.38589999079704285},{"id":"https://openalex.org/C188382862","wikidata":"https://www.wikidata.org/wiki/Q170430","display_name":"Predation","level":2,"score":0.3578000068664551},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.35659998655319214},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.350600004196167},{"id":"https://openalex.org/C110201527","wikidata":"https://www.wikidata.org/wiki/Q5508845","display_name":"Functional response","level":4,"score":0.33899998664855957},{"id":"https://openalex.org/C95713431","wikidata":"https://www.wikidata.org/wiki/Q631425","display_name":"Vulnerability (computing)","level":2,"score":0.3310999870300293},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.32350000739097595},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.3089999854564667},{"id":"https://openalex.org/C52079815","wikidata":"https://www.wikidata.org/wiki/Q7229808","display_name":"Population model","level":3,"score":0.27869999408721924},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.25929999351501465},{"id":"https://openalex.org/C47318914","wikidata":"https://www.wikidata.org/wiki/Q295872","display_name":"Ecological systems theory","level":2,"score":0.2563999891281128},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.2558000087738037},{"id":"https://openalex.org/C12064787","wikidata":"https://www.wikidata.org/wiki/Q4736552","display_name":"Alternative stable state","level":3,"score":0.25049999356269836}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1155/jama/9030706","is_oa":true,"landing_page_url":"https://doi.org/10.1155/jama/9030706","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1155/jama/9030706","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:34fd20cd2d764459b9d8964f312d2b5c","is_oa":true,"landing_page_url":"https://doaj.org/article/34fd20cd2d764459b9d8964f312d2b5c","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Applied Mathematics, Vol 2025 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/jama/9030706","is_oa":true,"landing_page_url":"https://doi.org/10.1155/jama/9030706","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1155/jama/9030706","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4416447451.pdf","grobid_xml":"https://content.openalex.org/works/W4416447451.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W1492544702","https://openalex.org/W1596429882","https://openalex.org/W2097732986","https://openalex.org/W2545712081","https://openalex.org/W3094076402","https://openalex.org/W3112595982","https://openalex.org/W3208295473","https://openalex.org/W4362473432","https://openalex.org/W4377861761","https://openalex.org/W4389425768","https://openalex.org/W4392024241","https://openalex.org/W4392782536","https://openalex.org/W4399708766","https://openalex.org/W4400115197","https://openalex.org/W4400451148","https://openalex.org/W4401358607","https://openalex.org/W4401435072","https://openalex.org/W4402349846","https://openalex.org/W4402513660","https://openalex.org/W4402625738","https://openalex.org/W4404378680","https://openalex.org/W4405064754","https://openalex.org/W4407850600","https://openalex.org/W4410332154","https://openalex.org/W4410609559","https://openalex.org/W4410989881"],"related_works":[],"abstract_inverted_index":{"This":[0],"study":[1,41],"explores":[2],"the":[3,11,17,43,57,90,103,107,132,142],"dynamics":[4,136],"of":[5,45,137,144],"a":[6],"prey\u2013predator":[7,138],"system":[8,91],"incorporating":[9],"both":[10,33],"Allee":[12,110,115,146],"and":[13,35,54,62,79,111,134,140,147],"refuge":[14,112,148],"effects":[15,149],"in":[16,31,150],"prey":[18,52],"population.":[19],"A":[20,67],"deterministic":[21],"mathematical":[22],"model":[23],"is":[24,72],"formulated":[25],"to":[26,74,125],"capture":[27],"these":[28],"ecological":[29,151],"phenomena,":[30],"which":[32],"analytical":[34],"numerical":[36,84],"properties":[37],"are":[38],"investigated.":[39],"The":[40,86],"establishes":[42],"existence":[44],"three":[46],"biologically":[47],"relevant":[48],"equilibria,":[49],"namely,":[50],"extinction,":[51],"only,":[53],"coexistence.":[55],"Moreover,":[56],"conditions":[58],"for":[59,76],"their":[60],"local":[61],"global":[63],"stability":[64,133],"were":[65],"derived.":[66],"Monte":[68],"Carlo":[69],"simulations":[70],"approach":[71],"applied":[73],"account":[75],"parameter":[77,104],"uncertainty":[78],"random":[80],"fluctuations,":[81],"revealing":[82],"key":[83],"behaviors.":[85],"results":[87,128],"demonstrate":[88],"that":[89],"may":[92],"exhibit":[93],"stable":[94],"coexistence,":[95],"oscillatory":[96],"dynamics,":[97],"or":[98],"limit":[99],"cycles":[100],"depending":[101],"on":[102],"values,":[105],"highlighting":[106],"interplay":[108],"between":[109],"effects.":[113],"Low":[114],"thresholds":[116,122],"enhance":[117],"population":[118],"resilience,":[119],"while":[120],"high":[121],"increase":[123],"vulnerability":[124],"collapse.":[126],"These":[127],"provide":[129],"insights":[130],"into":[131],"long\u2010term":[135],"interactions":[139],"highlight":[141],"importance":[143],"considering":[145],"management.":[152]},"counts_by_year":[],"updated_date":"2026-06-14T06:11:07.267592","created_date":"2025-11-23T00:00:00"}
