{"id":"https://openalex.org/W2997738099","doi":"https://doi.org/10.1142/s0218127419501955","title":"Modeling the Effect of Fear in a Prey\u2013Predator System with Prey Refuge and Gestation Delay","display_name":"Modeling the Effect of Fear in a Prey\u2013Predator System with Prey Refuge and Gestation Delay","publication_year":2019,"publication_date":"2019-12-26","ids":{"openalex":"https://openalex.org/W2997738099","doi":"https://doi.org/10.1142/s0218127419501955","mag":"2997738099"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127419501955","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127419501955","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/A5100734479","display_name":"Ankit Kumar","orcid":"https://orcid.org/0000-0002-2540-4488"},"institutions":[{"id":"https://openalex.org/I74796645","display_name":"Birla Institute of Technology and Science, Pilani","ror":"https://ror.org/001p3jz28","country_code":"IN","type":"education","lineage":["https://openalex.org/I74796645"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Ankit Kumar","raw_affiliation_strings":["Department of Mathematics, BITS Pilani, Pilani Campus, Pilani 333031, Rajasthan, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, BITS Pilani, Pilani Campus, Pilani 333031, Rajasthan, India","institution_ids":["https://openalex.org/I74796645"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5011919067","display_name":"Balram Dubey","orcid":"https://orcid.org/0000-0002-4009-2208"},"institutions":[{"id":"https://openalex.org/I74796645","display_name":"Birla Institute of Technology and Science, Pilani","ror":"https://ror.org/001p3jz28","country_code":"IN","type":"education","lineage":["https://openalex.org/I74796645"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Balram Dubey","raw_affiliation_strings":["Department of Mathematics, BITS Pilani, Pilani Campus, Pilani 333031, Rajasthan, India"],"raw_orcid":"https://orcid.org/0000-0002-4009-2208","affiliations":[{"raw_affiliation_string":"Department of Mathematics, BITS Pilani, Pilani Campus, Pilani 333031, Rajasthan, India","institution_ids":["https://openalex.org/I74796645"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I74796645"],"apc_list":null,"apc_paid":null,"fwci":4.8535,"has_fulltext":false,"cited_by_count":74,"citation_normalized_percentile":{"value":0.95144929,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"29","issue":"14","first_page":"1950195","last_page":"1950195"},"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":0.9997000098228455,"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":0.9997000098228455,"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":0.9922999739646912,"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":0.9684000015258789,"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/predation","display_name":"Predation","score":0.8138957023620605},{"id":"https://openalex.org/keywords/hopf-bifurcation","display_name":"Hopf bifurcation","score":0.6794348359107971},{"id":"https://openalex.org/keywords/functional-response","display_name":"Functional response","score":0.6364471316337585},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.6194177865982056},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6164879202842712},{"id":"https://openalex.org/keywords/limit-cycle","display_name":"Limit cycle","score":0.5774288177490234},{"id":"https://openalex.org/keywords/predator","display_name":"Predator","score":0.5770148038864136},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5566907525062561},{"id":"https://openalex.org/keywords/lyapunov-exponent","display_name":"Lyapunov exponent","score":0.5269457101821899},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.484060674905777},{"id":"https://openalex.org/keywords/bifurcation-diagram","display_name":"Bifurcation diagram","score":0.4356600046157837},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.3780576288700104},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3569863438606262},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.3141382932662964},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.2821224331855774},{"id":"https://openalex.org/keywords/ecology","display_name":"Ecology","score":0.2382502555847168},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2344495952129364},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1870478093624115},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10363319516181946},{"id":"https://openalex.org/keywords/demography","display_name":"Demography","score":0.09324941039085388},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.07495203614234924},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.06638875603675842}],"concepts":[{"id":"https://openalex.org/C188382862","wikidata":"https://www.wikidata.org/wiki/Q170430","display_name":"Predation","level":2,"score":0.8138957023620605},{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.6794348359107971},{"id":"https://openalex.org/C110201527","wikidata":"https://www.wikidata.org/wiki/Q5508845","display_name":"Functional response","level":4,"score":0.6364471316337585},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.6194177865982056},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6164879202842712},{"id":"https://openalex.org/C93357160","wikidata":"https://www.wikidata.org/wiki/Q1545916","display_name":"Limit cycle","level":3,"score":0.5774288177490234},{"id":"https://openalex.org/C96857902","wikidata":"https://www.wikidata.org/wiki/Q2138108","display_name":"Predator","level":3,"score":0.5770148038864136},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5566907525062561},{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.5269457101821899},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.484060674905777},{"id":"https://openalex.org/C86243350","wikidata":"https://www.wikidata.org/wiki/Q2595915","display_name":"Bifurcation diagram","level":4,"score":0.4356600046157837},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.3780576288700104},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3569863438606262},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.3141382932662964},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.2821224331855774},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.2382502555847168},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2344495952129364},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1870478093624115},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10363319516181946},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.09324941039085388},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.07495203614234924},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.06638875603675842},{"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/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127419501955","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127419501955","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":0.550000011920929}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":49,"referenced_works":["https://openalex.org/W290250603","https://openalex.org/W997355000","https://openalex.org/W1531715726","https://openalex.org/W1586658033","https://openalex.org/W1971188387","https://openalex.org/W1974792252","https://openalex.org/W1989574171","https://openalex.org/W1990521675","https://openalex.org/W1996961144","https://openalex.org/W2004191665","https://openalex.org/W2012393132","https://openalex.org/W2014352588","https://openalex.org/W2016097363","https://openalex.org/W2022666585","https://openalex.org/W2029879748","https://openalex.org/W2044779413","https://openalex.org/W2050000868","https://openalex.org/W2050082994","https://openalex.org/W2057583771","https://openalex.org/W2057585737","https://openalex.org/W2061491569","https://openalex.org/W2062203460","https://openalex.org/W2066620167","https://openalex.org/W2071923791","https://openalex.org/W2090249044","https://openalex.org/W2093796271","https://openalex.org/W2094032066","https://openalex.org/W2095537547","https://openalex.org/W2116611122","https://openalex.org/W2124428761","https://openalex.org/W2131915744","https://openalex.org/W2149740781","https://openalex.org/W2204235026","https://openalex.org/W2253872233","https://openalex.org/W2308473015","https://openalex.org/W2402691489","https://openalex.org/W2417974185","https://openalex.org/W2510340639","https://openalex.org/W2523020409","https://openalex.org/W2537001751","https://openalex.org/W2584550390","https://openalex.org/W2605308502","https://openalex.org/W2770845872","https://openalex.org/W2792139240","https://openalex.org/W2801588258","https://openalex.org/W2883121298","https://openalex.org/W2886479949","https://openalex.org/W4293079218","https://openalex.org/W4297918182"],"related_works":["https://openalex.org/W2000314388","https://openalex.org/W4367693366","https://openalex.org/W2905043181","https://openalex.org/W3184324514","https://openalex.org/W2036212567","https://openalex.org/W4311297143","https://openalex.org/W2070512385","https://openalex.org/W2001296105","https://openalex.org/W2555766691","https://openalex.org/W2123969946"],"abstract_inverted_index":{"Recently,":[0],"some":[1],"field":[2],"experiments":[3],"and":[4,42,65,70,84,88,147,177,184],"studies":[5],"show":[6],"that":[7,55,103,118],"predators":[8,64],"affect":[9],"prey":[10,20,27,43,56,69,109,122],"not":[11],"only":[12],"by":[13,74,179],"direct":[14],"killing,":[15],"they":[16],"induce":[17],"fear":[18,40,105],"in":[19,45,60,107,112,143],"which":[21],"reduces":[22],"the":[23,39,61,66,81,86,104,108,113,119,132,140,144,181],"reproduction":[24],"rate":[25],"of":[26,63,92,121,139,159,192],"species.":[28,133],"Considering":[29],"this":[30],"fact,":[31],"we":[32,135],"propose":[33],"a":[34,125],"mathematical":[35],"model":[36,153],"to":[37,167],"study":[38],"effect":[41,106],"refuge":[44,120],"prey\u2013predator":[46],"system":[47,94],"with":[48,165],"gestation":[49,137],"time":[50],"delay.":[51],"It":[52,97,115],"is":[53,72,98,116,128,170],"assumed":[54],"population":[57,123,142],"grows":[58],"logistically":[59],"absence":[62],"interaction":[67],"between":[68],"predator":[71,141],"followed":[73],"Crowley\u2013Martin":[75],"type":[76],"functional":[77],"response.":[78],"We":[79],"obtained":[80],"equilibrium":[82],"points":[83],"studied":[85],"local":[87],"global":[89,148],"asymptotic":[90,149],"behaviors":[91],"nondelayed":[93],"around":[95],"them.":[96],"observed":[99,176],"from":[100],"our":[101],"analysis":[102],"induces":[110],"Hopf-bifurcation":[111,164],"system.":[114],"concluded":[117],"under":[124],"threshold":[126],"level":[127],"lucrative":[129],"for":[130,151,189],"both":[131],"Further,":[134],"incorporate":[136],"delay":[138,168,193],"model.":[145],"Local":[146],"stabilities":[150],"delayed":[152],"are":[154,174],"carried":[155],"out.":[156],"The":[157],"existence":[158],"stable":[160],"limit":[161],"cycle":[162],"via":[163],"respect":[166],"parameter":[169],"established.":[171],"Chaotic":[172],"oscillations":[173],"also":[175],"confirmed":[178],"drawing":[180],"bifurcation":[182],"diagram":[183],"evaluating":[185],"maximum":[186],"Lyapunov":[187],"exponent":[188],"large":[190],"values":[191],"parameter.":[194]},"counts_by_year":[{"year":2026,"cited_by_count":6},{"year":2025,"cited_by_count":14},{"year":2024,"cited_by_count":17},{"year":2023,"cited_by_count":15},{"year":2022,"cited_by_count":10},{"year":2021,"cited_by_count":10},{"year":2020,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}