{"id":"https://openalex.org/W4206533582","doi":"https://doi.org/10.1155/2022/8238384","title":"Complex Dynamical Behavior of Holling\u2013Tanner Predator\u2010Prey Model with Cross\u2010Diffusion","display_name":"Complex Dynamical Behavior of Holling\u2013Tanner Predator\u2010Prey Model with Cross\u2010Diffusion","publication_year":2022,"publication_date":"2022-01-01","ids":{"openalex":"https://openalex.org/W4206533582","doi":"https://doi.org/10.1155/2022/8238384"},"language":"en","primary_location":{"id":"doi:10.1155/2022/8238384","is_oa":true,"landing_page_url":"http://doi.org/10.1155/2022/8238384","pdf_url":"https://downloads.hindawi.com/journals/complexity/2022/8238384.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/complexity/2022/8238384.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5081594674","display_name":"Caiyun Wang","orcid":"https://orcid.org/0000-0001-5056-7468"},"institutions":[{"id":"https://openalex.org/I28992388","display_name":"Xinzhou Teachers University","ror":"https://ror.org/01175g155","country_code":"CN","type":"education","lineage":["https://openalex.org/I28992388"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Caiyun Wang","raw_affiliation_strings":["Department of Mathematics, Xinzhou Teachers University, Xinzhou 034000, Shanxi, China","Department of Mathematics, Xinzhou Teachers University, Xinzhou 034000, Shanxi"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Xinzhou Teachers University, Xinzhou 034000, Shanxi, China","institution_ids":["https://openalex.org/I28992388"]},{"raw_affiliation_string":"Department of Mathematics, Xinzhou Teachers University, Xinzhou 034000, Shanxi","institution_ids":["https://openalex.org/I28992388"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110537334","display_name":"Yongyong Pei","orcid":null},"institutions":[{"id":"https://openalex.org/I28992388","display_name":"Xinzhou Teachers University","ror":"https://ror.org/01175g155","country_code":"CN","type":"education","lineage":["https://openalex.org/I28992388"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yongyong Pei","raw_affiliation_strings":["The Affiliated Foreign Language Middle School of Xinzhou Teachers University, Xinzhou 034000, Shanxi"],"affiliations":[{"raw_affiliation_string":"The Affiliated Foreign Language Middle School of Xinzhou Teachers University, Xinzhou 034000, Shanxi","institution_ids":["https://openalex.org/I28992388"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042728213","display_name":"Yaqun Niu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yaqun Niu","raw_affiliation_strings":["Department of Mathematics, Taiyuan University, Taiyuan 034000, Shanxi, China","Department of Mathematics, Taiyuan University, Taiyuan 034000, Shanxi"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Taiyuan University, Taiyuan 034000, Shanxi, China","institution_ids":[]},{"raw_affiliation_string":"Department of Mathematics, Taiyuan University, Taiyuan 034000, Shanxi","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102792968","display_name":"Ruiqiang He","orcid":"https://orcid.org/0000-0003-3355-4600"},"institutions":[{"id":"https://openalex.org/I28992388","display_name":"Xinzhou Teachers University","ror":"https://ror.org/01175g155","country_code":"CN","type":"education","lineage":["https://openalex.org/I28992388"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ruiqiang He","raw_affiliation_strings":["Department of Mathematics, Xinzhou Teachers University, Xinzhou 034000, Shanxi, China","Department of Mathematics, Xinzhou Teachers University, Xinzhou 034000, Shanxi"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Xinzhou Teachers University, Xinzhou 034000, Shanxi, China","institution_ids":["https://openalex.org/I28992388"]},{"raw_affiliation_string":"Department of Mathematics, Xinzhou Teachers University, Xinzhou 034000, Shanxi","institution_ids":["https://openalex.org/I28992388"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5081594674"],"corresponding_institution_ids":["https://openalex.org/I28992388"],"apc_list":{"value":2300,"currency":"USD","value_usd":2300},"apc_paid":{"value":2300,"currency":"USD","value_usd":2300},"fwci":0.3992,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.6086131,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"2022","issue":"1","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":0.9995999932289124,"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":0.9995999932289124,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9950000047683716,"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"}},{"id":"https://openalex.org/T11764","display_name":"Evolution and Genetic Dynamics","score":0.9927999973297119,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/predator","display_name":"Predator","score":0.6402757167816162},{"id":"https://openalex.org/keywords/pattern-formation","display_name":"Pattern formation","score":0.6342039704322815},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.6262078881263733},{"id":"https://openalex.org/keywords/predation","display_name":"Predation","score":0.6127772927284241},{"id":"https://openalex.org/keywords/spatial-ecology","display_name":"Spatial ecology","score":0.6042119264602661},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.5235592722892761},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.5182368755340576},{"id":"https://openalex.org/keywords/biological-system","display_name":"Biological system","score":0.4804955720901489},{"id":"https://openalex.org/keywords/turing","display_name":"Turing","score":0.4566452205181122},{"id":"https://openalex.org/keywords/common-spatial-pattern","display_name":"Common spatial pattern","score":0.4399193525314331},{"id":"https://openalex.org/keywords/spatiotemporal-pattern","display_name":"Spatiotemporal pattern","score":0.4288976192474365},{"id":"https://openalex.org/keywords/scale","display_name":"Scale (ratio)","score":0.4154580533504486},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3415166735649109},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3385869860649109},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.30586475133895874},{"id":"https://openalex.org/keywords/ecology","display_name":"Ecology","score":0.29873865842819214},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.24706321954727173},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.22718793153762817},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.22433346509933472}],"concepts":[{"id":"https://openalex.org/C96857902","wikidata":"https://www.wikidata.org/wiki/Q2138108","display_name":"Predator","level":3,"score":0.6402757167816162},{"id":"https://openalex.org/C207016750","wikidata":"https://www.wikidata.org/wiki/Q1955627","display_name":"Pattern formation","level":2,"score":0.6342039704322815},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.6262078881263733},{"id":"https://openalex.org/C188382862","wikidata":"https://www.wikidata.org/wiki/Q170430","display_name":"Predation","level":2,"score":0.6127772927284241},{"id":"https://openalex.org/C158709400","wikidata":"https://www.wikidata.org/wiki/Q3578586","display_name":"Spatial ecology","level":2,"score":0.6042119264602661},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.5235592722892761},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.5182368755340576},{"id":"https://openalex.org/C186060115","wikidata":"https://www.wikidata.org/wiki/Q30336093","display_name":"Biological system","level":1,"score":0.4804955720901489},{"id":"https://openalex.org/C9870796","wikidata":"https://www.wikidata.org/wiki/Q490481","display_name":"Turing","level":2,"score":0.4566452205181122},{"id":"https://openalex.org/C173727882","wikidata":"https://www.wikidata.org/wiki/Q5153620","display_name":"Common spatial pattern","level":2,"score":0.4399193525314331},{"id":"https://openalex.org/C2779108282","wikidata":"https://www.wikidata.org/wiki/Q22908968","display_name":"Spatiotemporal pattern","level":2,"score":0.4288976192474365},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.4154580533504486},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3415166735649109},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3385869860649109},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.30586475133895874},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.29873865842819214},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.24706321954727173},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.22718793153762817},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.22433346509933472},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2022/8238384","is_oa":true,"landing_page_url":"http://doi.org/10.1155/2022/8238384","pdf_url":"https://downloads.hindawi.com/journals/complexity/2022/8238384.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:3ca65969c6bc42028eaa791ec5833c6a","is_oa":true,"landing_page_url":"https://doaj.org/article/3ca65969c6bc42028eaa791ec5833c6a","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Complexity, Vol 2022 (2022)","raw_type":"article"},{"id":"pmh:oai:hindawi.com:10.1155/2022/8238384","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2022/8238384","pdf_url":null,"source":{"id":"https://openalex.org/S4306400340","display_name":"Hindawi Journal of Chemistry (Hindawi)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210126990","host_organization_name":"Hindawi (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210126990"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Research Article"}],"best_oa_location":{"id":"doi:10.1155/2022/8238384","is_oa":true,"landing_page_url":"http://doi.org/10.1155/2022/8238384","pdf_url":"https://downloads.hindawi.com/journals/complexity/2022/8238384.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2245674178","display_name":null,"funder_award_id":"XK201501","funder_id":"https://openalex.org/F4320328124","funder_display_name":"Xinzhou Teachers University"},{"id":"https://openalex.org/G709709921","display_name":null,"funder_award_id":"2019KY07","funder_id":"https://openalex.org/F4320328124","funder_display_name":"Xinzhou Teachers University"}],"funders":[{"id":"https://openalex.org/F4320328124","display_name":"Xinzhou Teachers University","ror":"https://ror.org/01175g155"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4206533582.pdf","grobid_xml":"https://content.openalex.org/works/W4206533582.grobid-xml"},"referenced_works_count":49,"referenced_works":["https://openalex.org/W1266034465","https://openalex.org/W1848156638","https://openalex.org/W1969978946","https://openalex.org/W1971171666","https://openalex.org/W1993604411","https://openalex.org/W1994681001","https://openalex.org/W1995775417","https://openalex.org/W1996961144","https://openalex.org/W2000897512","https://openalex.org/W2001451047","https://openalex.org/W2009948646","https://openalex.org/W2011882588","https://openalex.org/W2019404680","https://openalex.org/W2020628783","https://openalex.org/W2020896504","https://openalex.org/W2027665073","https://openalex.org/W2061423359","https://openalex.org/W2063840230","https://openalex.org/W2063840822","https://openalex.org/W2065355448","https://openalex.org/W2067748671","https://openalex.org/W2074610367","https://openalex.org/W2076123824","https://openalex.org/W2077585277","https://openalex.org/W2086222060","https://openalex.org/W2102265921","https://openalex.org/W2259564976","https://openalex.org/W2274351203","https://openalex.org/W2288899969","https://openalex.org/W2408833675","https://openalex.org/W2472612660","https://openalex.org/W2515040453","https://openalex.org/W2521286112","https://openalex.org/W2577347286","https://openalex.org/W2770299407","https://openalex.org/W2775318754","https://openalex.org/W2781057905","https://openalex.org/W2799487647","https://openalex.org/W2883043942","https://openalex.org/W2883710534","https://openalex.org/W2888218207","https://openalex.org/W2904982944","https://openalex.org/W2922136954","https://openalex.org/W2975608364","https://openalex.org/W3001560189","https://openalex.org/W3009294070","https://openalex.org/W3115856193","https://openalex.org/W4236990395","https://openalex.org/W4297918182"],"related_works":["https://openalex.org/W4389224764","https://openalex.org/W4361273936","https://openalex.org/W2015141095","https://openalex.org/W2101539302","https://openalex.org/W3214411012","https://openalex.org/W2158756521","https://openalex.org/W3150423926","https://openalex.org/W2020630196","https://openalex.org/W2132986211","https://openalex.org/W2149978615"],"abstract_inverted_index":{"Spatial":[0],"predator\u2010prey":[1,34],"models":[2],"have":[3],"been":[4],"studied":[5,37],"by":[6,43,73,121],"researchers":[7],"for":[8],"many":[9],"years,":[10],"because":[11],"the":[12,16,48,63,69,74,86,157,164,170],"exact":[13],"distributions":[14],"of":[15,30,55,68,77,85,116,126,140,152,167,172],"population":[17],"can":[18,118,161],"be":[19,58,119],"well":[20],"illustrated":[21],"via":[22,38],"pattern":[23,66,83,91,114],"formation.":[24],"In":[25],"this":[26],"paper,":[27],"amplitude":[28,44],"equations":[29],"a":[31,138],"spatial":[32],"Holling\u2013Tanner":[33],"model":[35],"are":[36,71],"multiple":[39],"scale":[40],"analysis.":[41],"First,":[42],"equations,":[45],"we":[46,61],"obtain":[47],"corresponding":[49],"intervals":[50],"in":[51,94,169],"which":[52],"different":[53],"kinds":[54],"patterns":[56,100,125,131,134],"will":[57],"onset.":[59],"Additionally,":[60],"get":[62],"conclusion":[64],"that":[65,113,123,149],"transitions":[67,84,115],"predator":[70,80,87,160],"induced":[72,120],"increasing":[75],"rate":[76],"conversion":[78],"into":[79],"biomass.":[81],"Specifically,":[82],"between":[88,156],"distinct":[89],"Turing":[90],"structures":[92],"vary":[93],"an":[95],"orderly":[96],"manner:":[97],"from":[98,129],"spotted":[99,130],"to":[101,106,132,137,163],"stripe":[102,133,143],"patterns,":[103],"and":[104,135,142,154,159],"finally":[105,136],"black\u2010eye":[107],"patterns.":[108,144],"Moreover,":[109],"it":[110,146],"is":[111,147],"discovered":[112],"prey":[117,127,158],"cross\u2010diffusion;":[122],"is,":[124],"transmit":[128],"mixture":[139],"spot":[141],"Meanwhile,":[145],"found":[148],"both":[150],"effects":[151],"cross\u2010diffusion":[153],"interaction":[155],"lead":[162],"complicated":[165],"phenomenon":[166],"dynamics":[168],"system":[171],"biology.":[173]},"counts_by_year":[{"year":2024,"cited_by_count":2}],"updated_date":"2026-03-16T09:10:04.655348","created_date":"2025-10-10T00:00:00"}