{"id":"https://openalex.org/W4386896214","doi":"https://doi.org/10.1142/s0218127423501316","title":"Impact of Fear on Searching Efficiency of Prey: A Prey\u2013Predator Model with Weak Allee Effect","display_name":"Impact of Fear on Searching Efficiency of Prey: A Prey\u2013Predator Model with Weak Allee Effect","publication_year":2023,"publication_date":"2023-09-15","ids":{"openalex":"https://openalex.org/W4386896214","doi":"https://doi.org/10.1142/s0218127423501316"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127423501316","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127423501316","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/A5050706821","display_name":"Sourav Kumar Sasmal","orcid":"https://orcid.org/0000-0002-0492-0635"},"institutions":[{"id":"https://openalex.org/I154851008","display_name":"Indian Institute of Technology Roorkee","ror":"https://ror.org/00582g326","country_code":"IN","type":"education","lineage":["https://openalex.org/I154851008"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Sourav Kumar Sasmal","raw_affiliation_strings":["Department of Applied Mathematics and Scientific Computing, IIT Roorkee, Uttarakhand \u2013 247667, India"],"raw_orcid":"https://orcid.org/0000-0002-0492-0635","affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Scientific Computing, IIT Roorkee, Uttarakhand \u2013 247667, India","institution_ids":["https://openalex.org/I154851008"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087774360","display_name":"Saheb Pal","orcid":"https://orcid.org/0000-0003-1867-2473"},"institutions":[{"id":"https://openalex.org/I130291710","display_name":"Visva-Bharati University","ror":"https://ror.org/02y28sc20","country_code":"IN","type":"education","lineage":["https://openalex.org/I130291710"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Saheb Pal","raw_affiliation_strings":["Department of Mathematics, Visva-Bharati, Santiniketan 731235, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Visva-Bharati, Santiniketan 731235, India","institution_ids":["https://openalex.org/I130291710"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5082194404","display_name":"Nikhil Pal","orcid":"https://orcid.org/0000-0002-6434-4545"},"institutions":[{"id":"https://openalex.org/I130291710","display_name":"Visva-Bharati University","ror":"https://ror.org/02y28sc20","country_code":"IN","type":"education","lineage":["https://openalex.org/I130291710"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Nikhil Pal","raw_affiliation_strings":["Department of Mathematics, Visva-Bharati, Santiniketan 731235, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Visva-Bharati, Santiniketan 731235, India","institution_ids":["https://openalex.org/I130291710"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5046784299","display_name":"Yasuhiro Takeuchi","orcid":"https://orcid.org/0000-0002-0847-5233"},"institutions":[{"id":"https://openalex.org/I131231118","display_name":"Aoyama Gakuin University","ror":"https://ror.org/002rw7y37","country_code":"JP","type":"education","lineage":["https://openalex.org/I131231118"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Yasuhiro Takeuchi","raw_affiliation_strings":["Department of Mathematical Sciences, Aoyama Gakuin University, Kanagawa 252-5258, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Aoyama Gakuin University, Kanagawa 252-5258, Japan","institution_ids":["https://openalex.org/I131231118"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5050706821"],"corresponding_institution_ids":["https://openalex.org/I154851008"],"apc_list":null,"apc_paid":null,"fwci":3.6087,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.93093326,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":99},"biblio":{"volume":"33","issue":"11","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":0.9998000264167786,"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":0.9998000264167786,"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":0.9980999827384949,"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/T11252","display_name":"Evolutionary Game Theory and Cooperation","score":0.9886999726295471,"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":0.9699216485023499},{"id":"https://openalex.org/keywords/predator","display_name":"Predator","score":0.6424955725669861},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.6392035484313965},{"id":"https://openalex.org/keywords/predation","display_name":"Predation","score":0.6198371648788452},{"id":"https://openalex.org/keywords/extinction","display_name":"Extinction (optical mineralogy)","score":0.5699148178100586},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5276328921318054},{"id":"https://openalex.org/keywords/hopf-bifurcation","display_name":"Hopf bifurcation","score":0.48349621891975403},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.46576476097106934},{"id":"https://openalex.org/keywords/carrying-capacity","display_name":"Carrying capacity","score":0.4628225266933441},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.4572070240974426},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.43399178981781006},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43085533380508423},{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.4177965819835663},{"id":"https://openalex.org/keywords/functional-response","display_name":"Functional response","score":0.41099289059638977},{"id":"https://openalex.org/keywords/ecology","display_name":"Ecology","score":0.3459938168525696},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.32965153455734253},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.19962593913078308},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.1817888617515564},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1658189594745636},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.15133056044578552}],"concepts":[{"id":"https://openalex.org/C10958125","wikidata":"https://www.wikidata.org/wiki/Q2301505","display_name":"Allee effect","level":3,"score":0.9699216485023499},{"id":"https://openalex.org/C96857902","wikidata":"https://www.wikidata.org/wiki/Q2138108","display_name":"Predator","level":3,"score":0.6424955725669861},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.6392035484313965},{"id":"https://openalex.org/C188382862","wikidata":"https://www.wikidata.org/wiki/Q170430","display_name":"Predation","level":2,"score":0.6198371648788452},{"id":"https://openalex.org/C101991246","wikidata":"https://www.wikidata.org/wiki/Q5422078","display_name":"Extinction (optical mineralogy)","level":2,"score":0.5699148178100586},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5276328921318054},{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.48349621891975403},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.46576476097106934},{"id":"https://openalex.org/C103781064","wikidata":"https://www.wikidata.org/wiki/Q866283","display_name":"Carrying capacity","level":2,"score":0.4628225266933441},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.4572070240974426},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.43399178981781006},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43085533380508423},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.4177965819835663},{"id":"https://openalex.org/C110201527","wikidata":"https://www.wikidata.org/wiki/Q5508845","display_name":"Functional response","level":4,"score":0.41099289059638977},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.3459938168525696},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.32965153455734253},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.19962593913078308},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.1817888617515564},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1658189594745636},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15133056044578552},{"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},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127423501316","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127423501316","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"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/15","display_name":"Life in Land","score":0.7599999904632568}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":47,"referenced_works":["https://openalex.org/W657833124","https://openalex.org/W943060623","https://openalex.org/W1542880507","https://openalex.org/W1965439315","https://openalex.org/W1966012509","https://openalex.org/W1969027200","https://openalex.org/W1995556171","https://openalex.org/W2004908709","https://openalex.org/W2010629222","https://openalex.org/W2022179617","https://openalex.org/W2035797868","https://openalex.org/W2048712240","https://openalex.org/W2054014123","https://openalex.org/W2056942998","https://openalex.org/W2060852353","https://openalex.org/W2063702754","https://openalex.org/W2065317320","https://openalex.org/W2068077597","https://openalex.org/W2072434909","https://openalex.org/W2079291463","https://openalex.org/W2079919864","https://openalex.org/W2081125336","https://openalex.org/W2082057759","https://openalex.org/W2091159659","https://openalex.org/W2106228428","https://openalex.org/W2107190886","https://openalex.org/W2126033810","https://openalex.org/W2131915744","https://openalex.org/W2138899304","https://openalex.org/W2152874168","https://openalex.org/W2158842610","https://openalex.org/W2162076259","https://openalex.org/W2168389674","https://openalex.org/W2308473015","https://openalex.org/W2315363230","https://openalex.org/W2506344596","https://openalex.org/W2618945985","https://openalex.org/W2639639281","https://openalex.org/W2883676107","https://openalex.org/W2884363819","https://openalex.org/W2889246061","https://openalex.org/W2943516434","https://openalex.org/W2954713868","https://openalex.org/W2971360585","https://openalex.org/W3173167187","https://openalex.org/W3184494791","https://openalex.org/W4293079218"],"related_works":["https://openalex.org/W4246753960","https://openalex.org/W2394047821","https://openalex.org/W1976102919","https://openalex.org/W4233118827","https://openalex.org/W2126719205","https://openalex.org/W2905043181","https://openalex.org/W3184324514","https://openalex.org/W2036212567","https://openalex.org/W4311297143","https://openalex.org/W2070512385"],"abstract_inverted_index":{"Reduced":[0],"population":[1,35,48,66],"growth":[2,29],"at":[3,160],"low":[4,257],"density":[5,89],"has":[6],"important":[7,264],"implications":[8],"for":[9,110],"conservation,":[10],"colonization":[11],"success,":[12],"and":[13,31,94,130,138,141,166,228,242],"wildlife":[14],"management.":[15],"In":[16],"this":[17],"context,":[18],"the":[19,23,64,68,74,79,105,120,128,153,173,203,245,268],"Allee":[20,70],"effect,":[21],"i.e.":[22],"positive":[24],"relationship":[25],"between":[26],"per":[27],"capita":[28],"rate":[30],"biomass":[32],"of":[33,82,117,132,156,270],"small":[34],"density,":[36],"is":[37,44,158,169,222,253],"a":[38,55,60,216,224],"crucial":[39],"biological":[40,265],"phenomenon":[41],"since":[42],"it":[43],"directly":[45],"related":[46],"to":[47,91,172,256],"extinction.":[49],"The":[50],"present":[51],"paper":[52],"deals":[53],"with":[54,59,87,175,211],"two-species":[56],"interacting":[57],"model":[58],"predator\u2013prey":[61,100,111],"relationship,":[62],"where":[63],"prey":[65,83,118,157],"experiences":[67],"mate-finding":[69],"effect":[71],"caused":[72],"by":[73,237],"predator.":[75,121],"We":[76,122,186,199,232],"assume":[77],"that":[78,151],"searching":[80],"efficiency":[81],"individuals":[84],"decreases":[85],"linearly":[86],"predator":[88],"due":[90],"predation":[92,97],"fear":[93],"investigate":[95],"how":[96,244],"intensity":[98],"affects":[99],"dynamics.":[101],"Moreover,":[102,260],"we":[103,149,261],"consider":[104],"Monod\u2013Haldane":[106],"type":[107],"functional":[108],"response":[109],"interactions,":[112],"which":[113,180],"shows":[114],"group":[115],"defense":[116],"against":[119],"provide":[123],"detailed":[124,146],"mathematical":[125,147],"analyses,":[126,148],"including":[127],"positivity":[129],"boundedness":[131],"solutions,":[133],"all":[134],"biologically":[135],"feasible":[136],"equilibria,":[137],"their":[139],"local":[140],"global":[142],"stabilities.":[143],"From":[144],"our":[145],"observe":[150],"when":[152,205,220,250],"carrying":[154,177,213,251,258],"capacity":[155,178,252],"low,":[159],"most":[161],"one":[162],"interior":[163,209,226],"equilibrium":[164,227],"exists,":[165],"system":[167,204,246],"dynamics":[168,247],"simple":[170],"compared":[171,255],"case":[174],"high":[176,212,254],"in":[179,202],"multiple":[181],"coexistence":[182],"equilibria":[183,210],"may":[184],"exist.":[185],"discuss":[187,262],"three":[188],"codimension-one":[189],"bifurcations":[190],"mathematically,":[191],"e.g.":[192,267],"Hopf":[193],"bifurcation,":[194,196],"transcritical":[195],"saddle-node":[197],"bifurcation.":[198],"notice":[200],"bistability":[201],"there":[206,221],"are":[207],"two":[208,239],"capacity.":[214,259],"However,":[215],"unique":[217],"attractor":[218],"exists":[219],"only":[223],"single":[225],"both":[229],"populations":[230],"persist.":[231],"perform":[233],"extensive":[234],"numerical":[235],"simulations":[236],"varying":[238],"parameters":[240],"simultaneously":[241],"explore":[243],"become":[248],"complex":[249],"other":[263],"phenomena,":[266],"paradox":[269],"enrichment,":[271],"bubbling":[272],"phenomenon,":[273],"etc.":[274]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":7}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}