{"id":"https://openalex.org/W4298007035","doi":"https://doi.org/10.1142/s0218127422501723","title":"Stability and Bifurcation Analysis of Two-Species Prey\u2013Predator Model Incorporating External Factors","display_name":"Stability and Bifurcation Analysis of Two-Species Prey\u2013Predator Model Incorporating External Factors","publication_year":2022,"publication_date":"2022-09-15","ids":{"openalex":"https://openalex.org/W4298007035","doi":"https://doi.org/10.1142/s0218127422501723"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127422501723","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127422501723","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/A5076354366","display_name":"M. Priyanka","orcid":null},"institutions":[{"id":"https://openalex.org/I880551032","display_name":"Gandhigram Rural Institute","ror":"https://ror.org/01abtgj51","country_code":"IN","type":"education","lineage":["https://openalex.org/I880551032"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"M. Priyanka","raw_affiliation_strings":["Department of Mathematics, The Gandhigram Rural Institute (Deemed to be University), Gandhigram-624 302, Tamil Nadu, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, The Gandhigram Rural Institute (Deemed to be University), Gandhigram-624 302, Tamil Nadu, India","institution_ids":["https://openalex.org/I880551032"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058574248","display_name":"P. Muthukumar","orcid":"https://orcid.org/0000-0003-1396-9948"},"institutions":[{"id":"https://openalex.org/I880551032","display_name":"Gandhigram Rural Institute","ror":"https://ror.org/01abtgj51","country_code":"IN","type":"education","lineage":["https://openalex.org/I880551032"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"P. Muthukumar","raw_affiliation_strings":["Department of Mathematics, The Gandhigram Rural Institute (Deemed to be University), Gandhigram-624 302, Tamil Nadu, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, The Gandhigram Rural Institute (Deemed to be University), Gandhigram-624 302, Tamil Nadu, India","institution_ids":["https://openalex.org/I880551032"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060837002","display_name":"Sachin Bhalekar","orcid":"https://orcid.org/0000-0003-1981-8171"},"institutions":[{"id":"https://openalex.org/I36893310","display_name":"University of Hyderabad","ror":"https://ror.org/04a7rxb17","country_code":"IN","type":"education","lineage":["https://openalex.org/I36893310"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Sachin Bhalekar","raw_affiliation_strings":["School of Mathematics and Statistics, University of Hyderabad, Hyderabad-500 046, India"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, University of Hyderabad, Hyderabad-500 046, India","institution_ids":["https://openalex.org/I36893310"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5076354366"],"corresponding_institution_ids":["https://openalex.org/I880551032"],"apc_list":null,"apc_paid":null,"fwci":0.7832,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.72587509,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"32","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":0.9998999834060669,"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":0.9998999834060669,"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":0.9929999709129333,"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/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.9679999947547913,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7236864566802979},{"id":"https://openalex.org/keywords/equilibrium-point","display_name":"Equilibrium point","score":0.622196614742279},{"id":"https://openalex.org/keywords/hopf-bifurcation","display_name":"Hopf bifurcation","score":0.5846992135047913},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.5725895166397095},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.5720801949501038},{"id":"https://openalex.org/keywords/saddle-node-bifurcation","display_name":"Saddle-node bifurcation","score":0.5324574112892151},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4999570846557617},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4939015507698059},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.4851135015487671},{"id":"https://openalex.org/keywords/transcritical-bifurcation","display_name":"Transcritical bifurcation","score":0.4149940013885498},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.26453346014022827},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.11103618144989014},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.10577505826950073},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09295684099197388},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07879796624183655}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7236864566802979},{"id":"https://openalex.org/C94766913","wikidata":"https://www.wikidata.org/wiki/Q1530271","display_name":"Equilibrium point","level":3,"score":0.622196614742279},{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.5846992135047913},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.5725895166397095},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.5720801949501038},{"id":"https://openalex.org/C101225446","wikidata":"https://www.wikidata.org/wiki/Q740190","display_name":"Saddle-node bifurcation","level":4,"score":0.5324574112892151},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4999570846557617},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4939015507698059},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.4851135015487671},{"id":"https://openalex.org/C55610538","wikidata":"https://www.wikidata.org/wiki/Q1502581","display_name":"Transcritical bifurcation","level":5,"score":0.4149940013885498},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.26453346014022827},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.11103618144989014},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.10577505826950073},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09295684099197388},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07879796624183655},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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/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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127422501723","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127422501723","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":[{"display_name":"Life in Land","score":0.46000000834465027,"id":"https://metadata.un.org/sdg/15"}],"awards":[{"id":"https://openalex.org/G7192885800","display_name":null,"funder_award_id":"F.510/7/DSA-1/2015(SAP-I)","funder_id":"https://openalex.org/F4320320767","funder_display_name":"University Grants Commission"}],"funders":[{"id":"https://openalex.org/F4320320767","display_name":"University Grants Commission","ror":"https://ror.org/04p800546"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W1977738976","https://openalex.org/W2051819235","https://openalex.org/W2062499133","https://openalex.org/W2474279756","https://openalex.org/W2781193798","https://openalex.org/W2883156073","https://openalex.org/W2905673345","https://openalex.org/W2935221474","https://openalex.org/W2954713868","https://openalex.org/W2978135155","https://openalex.org/W3005250610","https://openalex.org/W3006957419","https://openalex.org/W3010740471","https://openalex.org/W3036210048","https://openalex.org/W3092631372","https://openalex.org/W3093499569","https://openalex.org/W3100587479","https://openalex.org/W3106689908","https://openalex.org/W3106935897","https://openalex.org/W3117403338","https://openalex.org/W3125621822","https://openalex.org/W3138129580","https://openalex.org/W3152193037","https://openalex.org/W3165205998","https://openalex.org/W3165729882","https://openalex.org/W3171864068","https://openalex.org/W3215895292","https://openalex.org/W4220949616","https://openalex.org/W4282049560","https://openalex.org/W4293079218","https://openalex.org/W4296588043","https://openalex.org/W4298219840","https://openalex.org/W4310301864"],"related_works":["https://openalex.org/W4225624922","https://openalex.org/W3215350949","https://openalex.org/W257838698","https://openalex.org/W189436430","https://openalex.org/W2393929457","https://openalex.org/W2353805507","https://openalex.org/W2012700469","https://openalex.org/W2114785653","https://openalex.org/W2392834684","https://openalex.org/W2613793204"],"abstract_inverted_index":{"Constant":[0],"prey":[1,29,60],"refuge":[2,57],"with":[3,51,91],"immigration":[4,52],"and":[5,45,53],"harvesting":[6,54],"in":[7,12,15,32],"two":[8],"species":[9],"would":[10],"result":[11],"significant":[13],"diversity":[14],"the":[16,26,33,70,85,99,111,117,121,137,149],"dynamics":[17],"of":[18,28,35,84,98,113,139,151],"a":[19,36,47,92],"prey\u2013predator":[20,49],"population.":[21,38,61],"The":[22,108,131,141],"phrase":[23],"\u201crefuge\u201d":[24],"increases":[25],"likelihood":[27],"population":[30],"survival":[31],"face":[34],"predator":[37],"Based":[39],"on":[40],"these":[41],"findings,":[42],"we":[43],"created":[44],"examined":[46,90],"two-species":[48],"system":[50],"factors,":[55],"including":[56],"to":[58,161],"only":[59],"All":[62],"ecologically":[63],"possible":[64],"equilibrium":[65,87,123],"points":[66],"are":[67,125,159],"studied":[68],"for":[69,78,110,136,147],"proposed":[71,100],"system.":[72],"Routh\u2013Hurwitz":[73],"stability":[74,80,83],"criterion":[75],"is":[76,89,106,134,145],"used":[77],"local":[79],"analysis.":[81],"Global":[82],"interior":[86],"point":[88,124],"suitable":[93],"Lyapunov":[94,143],"function.":[95],"Local":[96],"bifurcation":[97,115],"system,":[101],"such":[102],"as":[103],"saddle-node":[104],"bifurcation,":[105],"analyzed.":[107],"conditions":[109],"emergence":[112],"this":[114],"at":[116],"critical":[118],"threshold":[119],"near":[120],"nonhyperbolic":[122],"established":[126],"by":[127],"utilizing":[128],"Sotomayor\u2019s":[129],"theorem.":[130],"transversality":[132],"condition":[133],"validated":[135],"occurrence":[138],"Hopf-bifurcation.":[140],"first":[142],"number":[144],"exploited":[146],"determining":[148],"nature":[150],"Hopf":[152],"bifurcating":[153],"periodic":[154],"solution.":[155],"Finally,":[156],"numerical":[157],"simulations":[158],"illustrated":[160],"validate":[162],"our":[163],"theoretical":[164],"predictions.":[165]},"counts_by_year":[{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
