{"id":"https://openalex.org/W4388104533","doi":"https://doi.org/10.1142/s0218127423501559","title":"Role of Allee Effect, Hunting Cooperation, and Dispersal to Prey\u2013Predator Model","display_name":"Role of Allee Effect, Hunting Cooperation, and Dispersal to Prey\u2013Predator Model","publication_year":2023,"publication_date":"2023-10-01","ids":{"openalex":"https://openalex.org/W4388104533","doi":"https://doi.org/10.1142/s0218127423501559"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127423501559","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127423501559","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/A5101596594","display_name":"Akanksha Akanksha","orcid":null},"institutions":[{"id":"https://openalex.org/I60054993","display_name":"Graphic Era University","ror":"https://ror.org/03wqgqd89","country_code":"IN","type":"education","lineage":["https://openalex.org/I60054993"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Akanksha","raw_affiliation_strings":["Department of Mathematics, Graphic Era Hill University, Dehradun 248002, Uttarakhand, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Graphic Era Hill University, Dehradun 248002, Uttarakhand, India","institution_ids":["https://openalex.org/I60054993"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017076535","display_name":"Shivam Shivam","orcid":null},"institutions":[{"id":"https://openalex.org/I60054993","display_name":"Graphic Era University","ror":"https://ror.org/03wqgqd89","country_code":"IN","type":"education","lineage":["https://openalex.org/I60054993"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Shivam","raw_affiliation_strings":["Department of Mathematics, Graphic Era (Deemed to be) University, Dehradun 248002, Uttarakhand, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Graphic Era (Deemed to be) University, Dehradun 248002, Uttarakhand, India","institution_ids":["https://openalex.org/I60054993"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060764666","display_name":"Sunil Kumar","orcid":"https://orcid.org/0000-0003-0620-1068"},"institutions":[{"id":"https://openalex.org/I60054993","display_name":"Graphic Era University","ror":"https://ror.org/03wqgqd89","country_code":"IN","type":"education","lineage":["https://openalex.org/I60054993"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Sunil Kumar","raw_affiliation_strings":["Department of Mathematics, Graphic Era Hill University, Dehradun 248002, Uttarakhand, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Graphic Era Hill University, Dehradun 248002, Uttarakhand, India","institution_ids":["https://openalex.org/I60054993"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5063105242","display_name":"Teekam Singh","orcid":"https://orcid.org/0000-0001-8050-5639"},"institutions":[{"id":"https://openalex.org/I60054993","display_name":"Graphic Era University","ror":"https://ror.org/03wqgqd89","country_code":"IN","type":"education","lineage":["https://openalex.org/I60054993"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Teekam Singh","raw_affiliation_strings":["Department of Computer Science and Engineering, Graphic Era (Deemed to be) University, Dehradun 248002, Uttarakhand, India"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering, Graphic Era (Deemed to be) University, Dehradun 248002, Uttarakhand, India","institution_ids":["https://openalex.org/I60054993"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5101596594"],"corresponding_institution_ids":["https://openalex.org/I60054993"],"apc_list":null,"apc_paid":null,"fwci":5.313,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.96154612,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"33","issue":"13","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":0.9973000288009644,"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":0.9937999844551086,"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":0.9951310753822327},{"id":"https://openalex.org/keywords/equilibrium-point","display_name":"Equilibrium point","score":0.6705330610275269},{"id":"https://openalex.org/keywords/biological-dispersal","display_name":"Biological dispersal","score":0.6428825259208679},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.6150673031806946},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5666635632514954},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5057787895202637},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.45891866087913513},{"id":"https://openalex.org/keywords/predation","display_name":"Predation","score":0.45763611793518066},{"id":"https://openalex.org/keywords/hopf-bifurcation","display_name":"Hopf bifurcation","score":0.4155736565589905},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.4054023027420044},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.36510226130485535},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3450365364551544},{"id":"https://openalex.org/keywords/ecology","display_name":"Ecology","score":0.2976447641849518},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2801128327846527},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.1991158425807953},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14502227306365967},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13275831937789917},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.11346477270126343},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.10453253984451294},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.10344898700714111},{"id":"https://openalex.org/keywords/demography","display_name":"Demography","score":0.07493796944618225}],"concepts":[{"id":"https://openalex.org/C10958125","wikidata":"https://www.wikidata.org/wiki/Q2301505","display_name":"Allee effect","level":3,"score":0.9951310753822327},{"id":"https://openalex.org/C94766913","wikidata":"https://www.wikidata.org/wiki/Q1530271","display_name":"Equilibrium point","level":3,"score":0.6705330610275269},{"id":"https://openalex.org/C47559259","wikidata":"https://www.wikidata.org/wiki/Q778143","display_name":"Biological dispersal","level":3,"score":0.6428825259208679},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.6150673031806946},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5666635632514954},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5057787895202637},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.45891866087913513},{"id":"https://openalex.org/C188382862","wikidata":"https://www.wikidata.org/wiki/Q170430","display_name":"Predation","level":2,"score":0.45763611793518066},{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.4155736565589905},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.4054023027420044},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.36510226130485535},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3450365364551544},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.2976447641849518},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2801128327846527},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.1991158425807953},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14502227306365967},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13275831937789917},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.11346477270126343},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.10453253984451294},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.10344898700714111},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.07493796944618225},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127423501559","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127423501559","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":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1604213221","https://openalex.org/W1977617303","https://openalex.org/W2022179617","https://openalex.org/W2064766682","https://openalex.org/W2065317320","https://openalex.org/W2067962826","https://openalex.org/W2086222060","https://openalex.org/W2105939751","https://openalex.org/W2584708840","https://openalex.org/W2899463402","https://openalex.org/W2929444604","https://openalex.org/W2941621557","https://openalex.org/W2948100916","https://openalex.org/W2954713868","https://openalex.org/W3087649035","https://openalex.org/W3110571211","https://openalex.org/W3111115752","https://openalex.org/W3136018011","https://openalex.org/W3171864068","https://openalex.org/W4200379918","https://openalex.org/W4283317569","https://openalex.org/W4285792222","https://openalex.org/W4362472089","https://openalex.org/W4366780230"],"related_works":["https://openalex.org/W2058467188","https://openalex.org/W3194217620","https://openalex.org/W4292054940","https://openalex.org/W2963652880","https://openalex.org/W3110571211","https://openalex.org/W3009292067","https://openalex.org/W4280534879","https://openalex.org/W2996217148","https://openalex.org/W2093153997","https://openalex.org/W4313856608"],"abstract_inverted_index":{"In":[0,33],"prey\u2013predator":[1,27,40],"interaction,":[2],"many":[3],"factors,":[4],"such":[5],"as":[6,152],"the":[7,19,29,39,62,65,75,82,87,94,103,110,113,129,135,156,161,165,171,190,202,214],"fear":[8],"effect,":[9,11,204],"Allee":[10,45,66,136,203],"cooperative":[12],"hunting,":[13],"and":[14,44,68,86,107,146,169,196,207],"group":[15],"behavior,":[16],"can":[17],"influence":[18],"population":[20,95],"dynamics.":[21],"Hence,":[22],"studying":[23],"these":[24],"factors":[25],"in":[26,47],"makes":[28],"model":[30,41,167],"more":[31],"realistic.":[32],"this":[34],"paper,":[35],"we":[36,72,163],"have":[37,56,73],"proposed":[38,104],"having":[42],"herd":[43],"effect":[46,67],"prey":[48],"population,":[49],"where":[50],"predators":[51],"follow":[52],"hunting":[53,69,141,205],"cooperation.":[54,70],"We":[55,100],"employed":[57],"temporal":[58,121],"analysis":[59,76,79,122],"to":[60,77,80,97,160,179,188,213],"examine":[61,81,164],"role":[63,83],"of":[64,84,89,112,158],"Furthermore,":[71],"extended":[74],"spatiotemporal":[78],"dispersal":[85],"type":[88],"spatial":[90,166],"structure":[91],"formed":[92],"by":[93,133],"due":[96],"random":[98],"movement.":[99],"first":[101],"discuss":[102],"model\u2019s":[105,215],"existence":[106],"positivity,":[108],"then":[109],"stability":[111,168],"existing":[114],"equilibrium":[115,131],"points":[116],"through":[117,126],"Routh\u2013Hurwitz":[118],"criteria.":[119],"The":[120,193],"is":[123],"carried":[124],"out":[125],"Hopf-bifurcation":[127],"at":[128],"coexistence":[130],"point":[132],"considering":[134],"threshold":[137],"([Formula:":[138,143,149],"see":[139,144,150],"text]),":[140,145],"cooperation":[142],"attack":[147],"rate":[148],"text])":[151],"controlled":[153],"parameters.":[154],"With":[155],"addition":[157],"diffusion":[159,208],"model,":[162],"derive":[170],"Turing":[172,181],"instability":[173],"condition,":[174],"which":[175],"will":[176],"give":[177],"rise":[178],"various":[180],"patterns.":[182],"Finally,":[183],"numerical":[184,197],"simulations":[185],"are":[186,210],"performed":[187],"validate":[189],"analytical":[191],"results.":[192],"theoretical":[194],"study":[195],"simulation":[198],"results":[199],"demonstrate":[200],"that":[201],"cooperation,":[206],"coefficient":[209],"sensitive":[211],"parameters":[212],"stability.":[216]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":11}],"updated_date":"2026-02-25T08:12:03.925757","created_date":"2025-10-10T00:00:00"}