{"id":"https://openalex.org/W4408911681","doi":"https://doi.org/10.1142/s0218127425500737","title":"Dynamics of a Predator\u2013Prey Model with Fear and Its Carryover Effects, Allee in Predator and Diffusion-Driven Patterns","display_name":"Dynamics of a Predator\u2013Prey Model with Fear and Its Carryover Effects, Allee in Predator and Diffusion-Driven Patterns","publication_year":2025,"publication_date":"2025-03-26","ids":{"openalex":"https://openalex.org/W4408911681","doi":"https://doi.org/10.1142/s0218127425500737"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127425500737","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127425500737","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/A5111332506","display_name":"Debjit Pal","orcid":null},"institutions":[{"id":"https://openalex.org/I170979836","display_name":"Jadavpur University","ror":"https://ror.org/02af4h012","country_code":"IN","type":"education","lineage":["https://openalex.org/I170979836"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Debjit Pal","raw_affiliation_strings":["Centre for Mathematical Biology and Ecology, Department of Mathematics, Jadavpur University, Kolkata 700032, West Bengal, India"],"raw_orcid":"https://orcid.org/0009-0001-8757-9283","affiliations":[{"raw_affiliation_string":"Centre for Mathematical Biology and Ecology, Department of Mathematics, Jadavpur University, Kolkata 700032, West Bengal, India","institution_ids":["https://openalex.org/I170979836"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009759131","display_name":"Dipak Kesh","orcid":"https://orcid.org/0000-0001-6979-6332"},"institutions":[{"id":"https://openalex.org/I170979836","display_name":"Jadavpur University","ror":"https://ror.org/02af4h012","country_code":"IN","type":"education","lineage":["https://openalex.org/I170979836"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Dipak Kesh","raw_affiliation_strings":["Centre for Mathematical Biology and Ecology, Department of Mathematics, Jadavpur University, Kolkata 700032, West Bengal, India"],"raw_orcid":"https://orcid.org/0000-0001-6979-6332","affiliations":[{"raw_affiliation_string":"Centre for Mathematical Biology and Ecology, Department of Mathematics, Jadavpur University, Kolkata 700032, West Bengal, India","institution_ids":["https://openalex.org/I170979836"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5041268622","display_name":"Debasis Mukherjee","orcid":"https://orcid.org/0000-0002-5149-5985"},"institutions":[{"id":"https://openalex.org/I34034455","display_name":"Ramakrishna Mission Vivekananda Educational and Research Institute","ror":"https://ror.org/03kp2qt98","country_code":"IN","type":"education","lineage":["https://openalex.org/I34034455"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Debasis Mukherjee","raw_affiliation_strings":["Department of Mathematics, Vivekananda College, Kolkata 700063, West Bengal, India"],"raw_orcid":"https://orcid.org/0000-0002-5149-5985","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Vivekananda College, Kolkata 700063, West Bengal, India","institution_ids":["https://openalex.org/I34034455"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":12.5057,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.98815762,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":100},"biblio":{"volume":"35","issue":"06","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":0.9550999999046326,"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":0.9550999999046326,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/allee-effect","display_name":"Allee effect","score":0.9734629392623901},{"id":"https://openalex.org/keywords/predator","display_name":"Predator","score":0.8301867246627808},{"id":"https://openalex.org/keywords/predation","display_name":"Predation","score":0.7707109451293945},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5200226306915283},{"id":"https://openalex.org/keywords/functional-response","display_name":"Functional response","score":0.4920327365398407},{"id":"https://openalex.org/keywords/dynamics","display_name":"Dynamics (music)","score":0.48390039801597595},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.45533671975135803},{"id":"https://openalex.org/keywords/ecology","display_name":"Ecology","score":0.38195550441741943},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.38070613145828247},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3543226718902588},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.2956913113594055},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.14401158690452576},{"id":"https://openalex.org/keywords/demography","display_name":"Demography","score":0.13489392399787903},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.10939708352088928}],"concepts":[{"id":"https://openalex.org/C10958125","wikidata":"https://www.wikidata.org/wiki/Q2301505","display_name":"Allee effect","level":3,"score":0.9734629392623901},{"id":"https://openalex.org/C96857902","wikidata":"https://www.wikidata.org/wiki/Q2138108","display_name":"Predator","level":3,"score":0.8301867246627808},{"id":"https://openalex.org/C188382862","wikidata":"https://www.wikidata.org/wiki/Q170430","display_name":"Predation","level":2,"score":0.7707109451293945},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5200226306915283},{"id":"https://openalex.org/C110201527","wikidata":"https://www.wikidata.org/wiki/Q5508845","display_name":"Functional response","level":4,"score":0.4920327365398407},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.48390039801597595},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.45533671975135803},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.38195550441741943},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.38070613145828247},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3543226718902588},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.2956913113594055},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14401158690452576},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.13489392399787903},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.10939708352088928},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127425500737","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127425500737","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":[],"awards":[{"id":"https://openalex.org/G8415830402","display_name":null,"funder_award_id":"09/0096(12492)/2021-EMR-I","funder_id":"https://openalex.org/F4320334740","funder_display_name":"Human Resource Development Group"}],"funders":[{"id":"https://openalex.org/F4320334740","display_name":"Human Resource Development Group","ror":"https://ror.org/0577j0g35"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":52,"referenced_works":["https://openalex.org/W1985072454","https://openalex.org/W1990242516","https://openalex.org/W2004191665","https://openalex.org/W2012279843","https://openalex.org/W2014352588","https://openalex.org/W2017329746","https://openalex.org/W2018940882","https://openalex.org/W2028644412","https://openalex.org/W2037459980","https://openalex.org/W2045212693","https://openalex.org/W2063516134","https://openalex.org/W2079291463","https://openalex.org/W2080880113","https://openalex.org/W2081642807","https://openalex.org/W2115226876","https://openalex.org/W2117974455","https://openalex.org/W2128938570","https://openalex.org/W2137315516","https://openalex.org/W2141111072","https://openalex.org/W2725162550","https://openalex.org/W2751562407","https://openalex.org/W2997738099","https://openalex.org/W2999426777","https://openalex.org/W3040459774","https://openalex.org/W3090218441","https://openalex.org/W3184494791","https://openalex.org/W3193961042","https://openalex.org/W3211371434","https://openalex.org/W4200617421","https://openalex.org/W4224276310","https://openalex.org/W4281930521","https://openalex.org/W4311123370","https://openalex.org/W4312002263","https://openalex.org/W4312204786","https://openalex.org/W4313648265","https://openalex.org/W4328142666","https://openalex.org/W4381053756","https://openalex.org/W4386240301","https://openalex.org/W4386491217","https://openalex.org/W4386577766","https://openalex.org/W4386634255","https://openalex.org/W4387906747","https://openalex.org/W4389494036","https://openalex.org/W4391022271","https://openalex.org/W4392558819","https://openalex.org/W4393258101","https://openalex.org/W4393326906","https://openalex.org/W4396709262","https://openalex.org/W4399019899","https://openalex.org/W4399240024","https://openalex.org/W4400548919","https://openalex.org/W4401115199"],"related_works":["https://openalex.org/W2168669462","https://openalex.org/W4390742005","https://openalex.org/W4233887507","https://openalex.org/W2954520391","https://openalex.org/W2061879675","https://openalex.org/W2192426841","https://openalex.org/W3160246123","https://openalex.org/W4309891670","https://openalex.org/W2163677464","https://openalex.org/W2103498027"],"abstract_inverted_index":{"Recent":[0],"research":[1,44],"suggests":[2],"that":[3,19,123],"the":[4,10,17,30,52,65,80,85,88,92,99,112,118,137,140,149,156,162,166,178,183,191,201,206,228,242,251,255,267,277,287],"presence":[5],"of":[6,13,87,117,152,158,194,203,272],"predator":[7,69],"may":[8],"affect":[9],"physical":[11],"characteristics":[12],"prey":[14,31,61,256],"species":[15,81,89],"to":[16,25,78,84,91,264],"level":[18],"it":[20],"is":[21,169],"more":[22],"effective":[23],"compared":[24],"direct":[26],"predation":[27],"in":[28,111,143,200,236,245,250,258,266,289],"reducing":[29],"biomass.":[32],"Furthermore,":[33],"such":[34,175],"nonlethal":[35],"impacts":[36],"might":[37],"persist":[38],"across":[39],"seasons":[40],"or":[41],"generations.":[42],"This":[43,71],"work":[45],"centers":[46],"on":[47,60,68,177],"a":[48],"predator\u2013prey":[49],"interaction":[50],"considering":[51],"predator\u2019s":[53,278],"fear":[54,132,153,172,195,252,273],"and":[55,76,104,133,160,190,196,217,241,274],"its":[56,134,197,275],"carryover":[57],"effects":[58],"(COEs)":[59],"as":[62,64],"well":[63],"Allee":[66,141,159,167,184,243,279],"effect":[67,142,157,168,244,253,280],"species.":[70],"model":[72],"incorporates":[73],"both":[74],"self-":[75],"cross-diffusions":[77],"explore":[79],"distribution":[82],"due":[83],"movement":[86],"subject":[90],"Neumann":[93],"boundary":[94],"condition.":[95],"First,":[96],"we":[97],"study":[98],"positivity,":[100],"boundedness,":[101],"feasible":[102],"equilibria":[103],"their":[105],"local":[106],"stability;":[107],"different":[108,218],"bifurcations":[109],"appear":[110],"nonspatial":[113],"system.":[114,150,268],"Global":[115],"dynamics":[116,225,271],"system":[119,163,179,187,224],"are":[120,221],"discussed,":[121],"showing":[122],"coexistence":[124],"equilibrium":[125],"can":[126,154],"never":[127],"be":[128],"globally":[129],"stable.":[130],"Both":[131],"COEs":[135,151,198,240],"destabilize":[136,161],"system,":[138],"but":[139,171,247],"predators,":[144,246],"once":[145],"destabilized,":[146],"again":[147],"stabilizes":[148],"influence":[155,193],"even":[164],"when":[165],"high,":[170],"has":[173],"no":[174],"impact":[176],"dynamics,":[180],"coupling":[181],"with":[182,238,282],"parameter.":[185],"The":[186,223,269],"exhibits":[188],"bistability,":[189],"combined":[192],"results":[199],"\u201cparadox":[202],"enrichment\u201d.":[204],"For":[205],"spatial":[207],"model,":[208],"Turing":[209],"instability":[210,216,219,262],"conditions,":[211],"wave":[212],"number":[213],"range":[214],"for":[215],"regions":[220],"derived.":[222],"permits":[226],"mainly":[227],"spot":[229],"stationary":[230],"patterns.":[231],"Diffusion":[232],"causes":[233],"an":[234,248],"increase":[235,249],"gatherings":[237,257],"rising":[239],"diminishes":[254],"specific":[259],"spots.":[260],"Hopf":[261],"leads":[263],"oscillation":[265],"delicate":[270],"COEs,":[276],"along":[281],"diffusion":[283],"reveal":[284],"insights":[285],"into":[286],"harmony":[288],"nature.":[290]},"counts_by_year":[{"year":2026,"cited_by_count":7},{"year":2025,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}