{"id":"https://openalex.org/W4306391237","doi":"https://doi.org/10.3390/math10203795","title":"Complex Dynamics of a Predator\u2013Prey Interaction with Fear Effect in Deterministic and Fluctuating Environments","display_name":"Complex Dynamics of a Predator\u2013Prey Interaction with Fear Effect in Deterministic and Fluctuating Environments","publication_year":2022,"publication_date":"2022-10-14","ids":{"openalex":"https://openalex.org/W4306391237","doi":"https://doi.org/10.3390/math10203795"},"language":"en","primary_location":{"id":"doi:10.3390/math10203795","doi":"https://doi.org/10.3390/math10203795","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/math10203795","pdf_url":"https://www.mdpi.com/2227-7390/10/20/3795/pdf?version=1666746570","source":{"id":"https://openalex.org/S4210192031","display_name":"Mathematics","issn_l":"2227-7390","issn":["2227-7390"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2227-7390/10/20/3795/pdf?version=1666746570","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5024867288","display_name":"Nirapada Santra","orcid":"https://orcid.org/0000-0002-1820-7451","observed_orcids":["https://orcid.org/0000-0002-1820-7451"]},"institutions":[{"id":"https://openalex.org/I98365261","display_name":"Indian Institute of Engineering Science and Technology, Shibpur","ror":"https://ror.org/02ytfzr55","country_code":"IN","type":"education","lineage":["https://openalex.org/I98365261"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Nirapada Santra","raw_affiliation_strings":["Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah 711103, India"],"raw_orcid":"https://orcid.org/0000-0002-1820-7451","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah 711103, India","institution_ids":["https://openalex.org/I98365261"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033826823","display_name":"Sudeshna Mondal","orcid":"https://orcid.org/0000-0001-8300-1591","observed_orcids":["https://orcid.org/0000-0001-8300-1591"]},"institutions":[{"id":"https://openalex.org/I98365261","display_name":"Indian Institute of Engineering Science and Technology, Shibpur","ror":"https://ror.org/02ytfzr55","country_code":"IN","type":"education","lineage":["https://openalex.org/I98365261"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Sudeshna Mondal","raw_affiliation_strings":["Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah 711103, India"],"raw_orcid":"https://orcid.org/0000-0001-8300-1591","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah 711103, India","institution_ids":["https://openalex.org/I98365261"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5028309399","display_name":"G. P. Samanta","orcid":"https://orcid.org/0000-0002-2956-6265","observed_orcids":["https://orcid.org/0000-0002-2956-6265"]},"institutions":[{"id":"https://openalex.org/I98365261","display_name":"Indian Institute of Engineering Science and Technology, Shibpur","ror":"https://ror.org/02ytfzr55","country_code":"IN","type":"education","lineage":["https://openalex.org/I98365261"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Guruprasad Samanta","raw_affiliation_strings":["Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah 711103, India"],"raw_orcid":"https://orcid.org/0000-0002-2956-6265","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah 711103, India","institution_ids":["https://openalex.org/I98365261"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5028309399"],"corresponding_institution_ids":["https://openalex.org/I98365261"],"apc_list":{"value":1800,"currency":"CHF","value_usd":1885},"apc_paid":{"value":1800,"currency":"CHF","value_usd":1885},"fwci":1.836,"has_fulltext":true,"cited_by_count":11,"citation_normalized_percentile":{"value":0.83266683,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":93,"max":97},"biblio":{"volume":"10","issue":"20","first_page":"3795","last_page":"3795"},"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":1.0,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T13377","display_name":"Ecosystem dynamics and resilience","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2306","display_name":"Global and Planetary Change"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11913","display_name":"Animal Ecology and Behavior Studies","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2303","display_name":"Ecology"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/predator-prey-interactions","display_name":"predator-prey interactions","score":0.9089999794960022},{"id":"https://openalex.org/keywords/fear-effect","display_name":"fear effect","score":0.8799999952316284},{"id":"https://openalex.org/keywords/antipredator-behavior","display_name":"antipredator behavior","score":0.9470000267028809},{"id":"https://openalex.org/keywords/gestation-delay","display_name":"gestation delay","score":0.8349999785423279},{"id":"https://openalex.org/keywords/paradox-of-enrichment","display_name":"paradox of enrichment","score":0.7680000066757202},{"id":"https://openalex.org/keywords/global-stability","display_name":"global stability","score":0.7599999904632568},{"id":"https://openalex.org/keywords/delay-differential-equations","display_name":"delay differential equations","score":0.6890000104904175},{"id":"https://openalex.org/keywords/stochastic-modeling","display_name":"stochastic modeling","score":0.5699999928474426},{"id":"https://openalex.org/keywords/white-gaussian-noise","display_name":"Gaussian white noise","score":0.875},{"id":"https://openalex.org/keywords/environmental-variability","display_name":"environmental variability","score":0.9039999842643738},{"id":"https://openalex.org/keywords/carrying-capacity","display_name":"carrying capacity","score":0.9100000262260437}],"concepts":[{"id":"https://openalex.org/C188382862","wikidata":"https://www.wikidata.org/wiki/Q170430","display_name":"Predation","level":2,"score":0.7213216423988342},{"id":"https://openalex.org/C96857902","wikidata":"https://www.wikidata.org/wiki/Q2138108","display_name":"Predator","level":3,"score":0.7134745121002197},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.49903440475463867},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.49289941787719727},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.48859864473342896},{"id":"https://openalex.org/C94766913","wikidata":"https://www.wikidata.org/wiki/Q1530271","display_name":"Equilibrium point","level":3,"score":0.47054749727249146},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3995038866996765},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.32381200790405273},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.31226596236228943},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3047146797180176},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.28136587142944336},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.262826144695282},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1709335446357727},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12749743461608887},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.08195444941520691},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08096367120742798},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"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/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/math10203795","doi":"https://doi.org/10.3390/math10203795","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/math10203795","pdf_url":"https://www.mdpi.com/2227-7390/10/20/3795/pdf?version=1666746570","source":{"id":"https://openalex.org/S4210192031","display_name":"Mathematics","issn_l":"2227-7390","issn":["2227-7390"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:gam:jmathe:v:10:y:2022:i:20:p:3795-:d:942684","doi":null,"is_oa":false,"landing_page_url":"https://www.mdpi.com/2227-7390/10/20/3795/","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,"listed_in":[],"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"},{"id":"pmh:oai:doaj.org/article:e97469f997984f438000740821b825ff","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/e97469f997984f438000740821b825ff","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,"listed_in":[],"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":"Mathematics, Vol 10, Iss 20, p 3795 (2022)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/math10203795","doi":"https://doi.org/10.3390/math10203795","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/math10203795","pdf_url":"https://www.mdpi.com/2227-7390/10/20/3795/pdf?version=1666746570","source":{"id":"https://openalex.org/S4210192031","display_name":"Mathematics","issn_l":"2227-7390","issn":["2227-7390"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4306391237.pdf","grobid_xml":"https://content.openalex.org/works/W4306391237.grobid-xml"},"referenced_works_count":41,"referenced_works":["https://openalex.org/W1969027200","https://openalex.org/W1973118029","https://openalex.org/W1974538767","https://openalex.org/W1978691980","https://openalex.org/W2001888401","https://openalex.org/W2004191665","https://openalex.org/W2014352588","https://openalex.org/W2015135859","https://openalex.org/W2017329746","https://openalex.org/W2020975304","https://openalex.org/W2027665073","https://openalex.org/W2050479020","https://openalex.org/W2054949701","https://openalex.org/W2061423359","https://openalex.org/W2066620167","https://openalex.org/W2079291463","https://openalex.org/W2114090429","https://openalex.org/W2121239718","https://openalex.org/W2126183035","https://openalex.org/W2128938570","https://openalex.org/W2131915744","https://openalex.org/W2139824906","https://openalex.org/W2163947014","https://openalex.org/W2173807495","https://openalex.org/W2308473015","https://openalex.org/W2625711953","https://openalex.org/W2893726567","https://openalex.org/W2900603914","https://openalex.org/W2935221474","https://openalex.org/W3006644109","https://openalex.org/W3010740471","https://openalex.org/W3012236243","https://openalex.org/W3022358134","https://openalex.org/W3091171793","https://openalex.org/W3166484709","https://openalex.org/W3190216985","https://openalex.org/W3193961042","https://openalex.org/W4200617421","https://openalex.org/W4210932856","https://openalex.org/W4237997615","https://openalex.org/W4250716583"],"related_works":["https://openalex.org/W4411451737","https://openalex.org/W4402936142","https://openalex.org/W4296360179","https://openalex.org/W3158686186","https://openalex.org/W4295037461","https://openalex.org/W4224991274","https://openalex.org/W7117685817","https://openalex.org/W3080375667","https://openalex.org/W2616496375","https://openalex.org/W4315574374"],"abstract_inverted_index":{"Many":[0],"ecological":[1,42],"models":[2],"have":[3,16,127],"received":[4],"much":[5],"attention":[6],"in":[7,67,139],"the":[8,31,37,48,55,81,109,131,179],"past":[9],"few":[10],"years.":[11],"In":[12,71],"particular,":[13],"predator\u2013prey":[14,77],"interactions":[15],"been":[17,128],"examined":[18],"from":[19],"many":[20],"angles":[21],"to":[22,54,137,177,190],"capture":[23],"and":[24,88,111,122,158,174],"explain":[25],"various":[26],"environmental":[27,90],"phenomena":[28],"meaningfully.":[29],"Although":[30],"consumption":[32],"of":[33,50,57,83,93,108,118,133,146,181],"prey":[34,69,86,94,101],"directly":[35],"by":[36,60,106],"predator":[38,110,112],"is":[39,135],"a":[40,76,182,191],"well-known":[41],"phenomenon,":[43],"theoretical":[44],"biologists":[45],"suggest":[46],"that":[47,79],"impact":[49],"anti-predator":[51],"behavior":[52],"due":[53],"fear":[56,84,107,157],"predators":[58],"(felt":[59],"prey)":[61],"can":[62],"be":[63],"even":[64],"more":[65],"crucial":[66],"shaping":[68],"demography.":[70],"this":[72],"article,":[73],"we":[74,151,168,185],"develop":[75],"model":[78,193],"considers":[80],"effects":[82],"on":[85,89,161],"reproduction":[87],"carrying":[91],"capacity":[92],"species.":[95],"We":[96],"also":[97,169],"include":[98],"two":[99],"delays:":[100],"species":[102],"birth":[103],"delay":[104,148],"influenced":[105],"gestation":[113],"delay.":[114],"The":[115],"global":[116],"stability":[117],"each":[119],"equilibrium":[120],"point":[121],"its":[123],"basic":[124],"dynamical":[125],"features":[126],"investigated.":[129],"Furthermore,":[130],"\u201cparadox":[132],"enrichment\u201d":[134],"shown":[136],"exist":[138],"our":[140,144,166,187],"system.":[141],"By":[142],"analysing":[143],"system":[145,189],"nonlinear":[147],"differential":[149],"equations,":[150],"gain":[152],"some":[153,171],"insights":[154],"into":[155],"how":[156],"delays":[159],"affect":[160],"population":[162],"dynamics.":[163],"To":[164],"demonstrate":[165],"findings,":[167],"perform":[170],"numerical":[172],"computations":[173],"simulations.":[175],"Finally,":[176],"evaluate":[178],"influence":[180],"fluctuating":[183],"environment,":[184],"compare":[186],"proposed":[188],"stochastic":[192],"with":[194],"Gaussian":[195],"white":[196],"noise":[197],"terms.":[198]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":4}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2022-10-17T00:00:00"}
