{"id":"https://openalex.org/W2898278399","doi":"https://doi.org/10.1142/s0218127418501407","title":"Bifurcations and Pattern Formation in a Predator\u2013Prey Model","display_name":"Bifurcations and Pattern Formation in a Predator\u2013Prey Model","publication_year":2018,"publication_date":"2018-10-01","ids":{"openalex":"https://openalex.org/W2898278399","doi":"https://doi.org/10.1142/s0218127418501407","mag":"2898278399"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127418501407","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127418501407","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/A5057599058","display_name":"Yongli Cai","orcid":"https://orcid.org/0000-0002-9461-1157"},"institutions":[{"id":"https://openalex.org/I4210147117","display_name":"Huaiyin Normal University","ror":"https://ror.org/03xvggv44","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210147117"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yongli Cai","raw_affiliation_strings":["School of Mathematical Science, Huaiyin Normal University, Huaian 223300, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Science, Huaiyin Normal University, Huaian 223300, P. R. China","institution_ids":["https://openalex.org/I4210147117"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111526999","display_name":"Zhanji Gui","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhanji Gui","raw_affiliation_strings":["Software Department, Hainan College of Software Technology, Qionghai 571400, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Software Department, Hainan College of Software Technology, Qionghai 571400, P. R. China","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100745894","display_name":"Xuebing Zhang","orcid":"https://orcid.org/0000-0003-0561-5576"},"institutions":[{"id":"https://openalex.org/I200845125","display_name":"Nanjing University of Information Science and Technology","ror":"https://ror.org/02y0rxk19","country_code":"CN","type":"education","lineage":["https://openalex.org/I200845125"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xuebing Zhang","raw_affiliation_strings":["College of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, P. R. China","institution_ids":["https://openalex.org/I200845125"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091670895","display_name":"Hongbo Shi","orcid":"https://orcid.org/0000-0001-9400-1415"},"institutions":[{"id":"https://openalex.org/I4210147117","display_name":"Huaiyin Normal University","ror":"https://ror.org/03xvggv44","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210147117"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hongbo Shi","raw_affiliation_strings":["School of Mathematical Science, Huaiyin Normal University, Huaian 223300, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Science, Huaiyin Normal University, Huaian 223300, P. R. China","institution_ids":["https://openalex.org/I4210147117"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100342178","display_name":"Weiming Wang","orcid":"https://orcid.org/0000-0002-7562-8260"},"institutions":[{"id":"https://openalex.org/I4210147117","display_name":"Huaiyin Normal University","ror":"https://ror.org/03xvggv44","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210147117"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Weiming Wang","raw_affiliation_strings":["School of Mathematical Science, Huaiyin Normal University, Huaian 223300, P. R. China"],"raw_orcid":"https://orcid.org/0000-0002-7562-8260","affiliations":[{"raw_affiliation_string":"School of Mathematical Science, Huaiyin Normal University, Huaian 223300, P. R. China","institution_ids":["https://openalex.org/I4210147117"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5057599058"],"corresponding_institution_ids":["https://openalex.org/I4210147117"],"apc_list":null,"apc_paid":null,"fwci":6.0241,"has_fulltext":false,"cited_by_count":43,"citation_normalized_percentile":{"value":0.96460885,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"28","issue":"11","first_page":"1850140","last_page":"1850140"},"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":0.9998000264167786,"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":0.9998000264167786,"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":0.9950000047683716,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9948999881744385,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/biological-applications-of-bifurcation-theory","display_name":"Biological applications of bifurcation theory","score":0.7801144123077393},{"id":"https://openalex.org/keywords/transcritical-bifurcation","display_name":"Transcritical bifurcation","score":0.7684012651443481},{"id":"https://openalex.org/keywords/saddle-node-bifurcation","display_name":"Saddle-node bifurcation","score":0.7549388408660889},{"id":"https://openalex.org/keywords/pitchfork-bifurcation","display_name":"Pitchfork bifurcation","score":0.7456979751586914},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7276002168655396},{"id":"https://openalex.org/keywords/bogdanov\u2013takens-bifurcation","display_name":"Bogdanov\u2013Takens bifurcation","score":0.715927004814148},{"id":"https://openalex.org/keywords/bifurcation-diagram","display_name":"Bifurcation diagram","score":0.6679950952529907},{"id":"https://openalex.org/keywords/hopf-bifurcation","display_name":"Hopf bifurcation","score":0.651498019695282},{"id":"https://openalex.org/keywords/homoclinic-bifurcation","display_name":"Homoclinic bifurcation","score":0.5999088883399963},{"id":"https://openalex.org/keywords/period-doubling-bifurcation","display_name":"Period-doubling bifurcation","score":0.5229014754295349},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.5073010325431824},{"id":"https://openalex.org/keywords/neumann-boundary-condition","display_name":"Neumann boundary condition","score":0.49166280031204224},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.48277178406715393},{"id":"https://openalex.org/keywords/center-manifold","display_name":"Center manifold","score":0.48001331090927124},{"id":"https://openalex.org/keywords/bifurcation-theory","display_name":"Bifurcation theory","score":0.4767252504825592},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.21212300658226013},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.15116873383522034},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.08952939510345459}],"concepts":[{"id":"https://openalex.org/C174914120","wikidata":"https://www.wikidata.org/wiki/Q4914973","display_name":"Biological applications of bifurcation theory","level":5,"score":0.7801144123077393},{"id":"https://openalex.org/C55610538","wikidata":"https://www.wikidata.org/wiki/Q1502581","display_name":"Transcritical bifurcation","level":5,"score":0.7684012651443481},{"id":"https://openalex.org/C101225446","wikidata":"https://www.wikidata.org/wiki/Q740190","display_name":"Saddle-node bifurcation","level":4,"score":0.7549388408660889},{"id":"https://openalex.org/C155092403","wikidata":"https://www.wikidata.org/wiki/Q1785924","display_name":"Pitchfork bifurcation","level":5,"score":0.7456979751586914},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7276002168655396},{"id":"https://openalex.org/C22257346","wikidata":"https://www.wikidata.org/wiki/Q4937510","display_name":"Bogdanov\u2013Takens bifurcation","level":5,"score":0.715927004814148},{"id":"https://openalex.org/C86243350","wikidata":"https://www.wikidata.org/wiki/Q2595915","display_name":"Bifurcation diagram","level":4,"score":0.6679950952529907},{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.651498019695282},{"id":"https://openalex.org/C155405617","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Homoclinic bifurcation","level":5,"score":0.5999088883399963},{"id":"https://openalex.org/C194271172","wikidata":"https://www.wikidata.org/wiki/Q2181373","display_name":"Period-doubling bifurcation","level":4,"score":0.5229014754295349},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.5073010325431824},{"id":"https://openalex.org/C163681178","wikidata":"https://www.wikidata.org/wiki/Q1149279","display_name":"Neumann boundary condition","level":3,"score":0.49166280031204224},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.48277178406715393},{"id":"https://openalex.org/C74774103","wikidata":"https://www.wikidata.org/wiki/Q4504202","display_name":"Center manifold","level":5,"score":0.48001331090927124},{"id":"https://openalex.org/C85075877","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Bifurcation theory","level":4,"score":0.4767252504825592},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.21212300658226013},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15116873383522034},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.08952939510345459},{"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/s0218127418501407","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127418501407","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 below water","id":"https://metadata.un.org/sdg/14","score":0.44999998807907104}],"awards":[{"id":"https://openalex.org/G4513732839","display_name":null,"funder_award_id":"61772017","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4815102976","display_name":null,"funder_award_id":"61672013","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6422570255","display_name":null,"funder_award_id":"11601179","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321605","display_name":"Government of Jiangsu Province","ror":"https://ror.org/004svx814"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W1531715726","https://openalex.org/W1848156638","https://openalex.org/W1968748439","https://openalex.org/W1980661496","https://openalex.org/W1986023394","https://openalex.org/W1990042727","https://openalex.org/W1992686598","https://openalex.org/W2001451047","https://openalex.org/W2006353561","https://openalex.org/W2007137093","https://openalex.org/W2025007427","https://openalex.org/W2028610578","https://openalex.org/W2029553241","https://openalex.org/W2032214168","https://openalex.org/W2038105662","https://openalex.org/W2040315865","https://openalex.org/W2040712046","https://openalex.org/W2050900164","https://openalex.org/W2054239928","https://openalex.org/W2056334019","https://openalex.org/W2064706206","https://openalex.org/W2069119945","https://openalex.org/W2078019615","https://openalex.org/W2108337779","https://openalex.org/W2152817052","https://openalex.org/W2219083431","https://openalex.org/W2259564976","https://openalex.org/W2317439655","https://openalex.org/W2468958630","https://openalex.org/W2577347286","https://openalex.org/W2763724627","https://openalex.org/W2765856888","https://openalex.org/W2767133619","https://openalex.org/W2775318754","https://openalex.org/W2789865014"],"related_works":["https://openalex.org/W2025138898","https://openalex.org/W2356715721","https://openalex.org/W2019027784","https://openalex.org/W2110197045","https://openalex.org/W1982778171","https://openalex.org/W2775656422","https://openalex.org/W2078078632","https://openalex.org/W4392057445","https://openalex.org/W1976081455","https://openalex.org/W1594652328"],"abstract_inverted_index":{"In":[0,41],"this":[1],"paper,":[2],"we":[3,57,81,105],"investigate":[4],"the":[5,19,34,39,42,48,53,59,69,75,83,86,108,165,169],"spatiotemporal":[6,147],"dynamics":[7],"of":[8,38,44,64,71,85,126,144],"a":[9,14],"Leslie\u2013Gower":[10],"predator\u2013prey":[11,170],"model":[12,109],"incorporating":[13],"prey":[15],"refuge":[16],"subject":[17],"to":[18],"Neumann":[20],"boundary":[21],"conditions.":[22],"We":[23],"mainly":[24],"consider":[25],"Hopf":[26,45,135],"bifurcation":[27,30,60,79,98,136,152],"and":[28,52,62,77,89,99,124,142,146,159],"steady-state":[29,37,72,87],"which":[31,119,137,153],"bifurcate":[32],"from":[33],"constant":[35],"positive":[36],"model.":[40,171],"case":[43,70],"bifurcation,":[46,73,88],"by":[47,74,117,134,150],"center":[49],"manifold":[50],"theory":[51],"normal":[54],"form":[55],"method,":[56],"establish":[58],"direction":[61],"stability":[63],"bifurcating":[65],"periodic":[66,131],"solutions;":[67],"in":[68,168],"local":[76],"global":[78],"theories,":[80],"prove":[82],"existence":[84],"find":[90,106],"that":[91,107],"there":[92],"are":[93],"two":[94],"typical":[95],"bifurcations,":[96],"Turing":[97,114],"Turing\u2013Hopf":[100,151],"bifurcation.":[101],"Via":[102],"numerical":[103],"simulations,":[104],"exhibits":[110],"not":[111],"only":[112],"stationary":[113],"pattern":[115,132,148,166],"induced":[116,133,149],"diffusion":[118],"is":[120,138,154],"dependent":[121,139,155],"on":[122,140,156],"space":[123],"independent":[125,143],"time,":[127],"but":[128],"also":[129],"temporal":[130],"time":[141,158],"space,":[145],"both":[157],"space.":[160],"These":[161],"results":[162],"may":[163],"enrich":[164],"formation":[167]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":11},{"year":2019,"cited_by_count":13}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
