{"id":"https://openalex.org/W2731338476","doi":"https://doi.org/10.1142/s0218127417500882","title":"Cross-Diffusion Induced Turing Instability and Amplitude Equation for a Toxic-Phytoplankton\u2013Zooplankton Model with Nonmonotonic Functional Response","display_name":"Cross-Diffusion Induced Turing Instability and Amplitude Equation for a Toxic-Phytoplankton\u2013Zooplankton Model with Nonmonotonic Functional Response","publication_year":2017,"publication_date":"2017-06-15","ids":{"openalex":"https://openalex.org/W2731338476","doi":"https://doi.org/10.1142/s0218127417500882","mag":"2731338476"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127417500882","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127417500882","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/A5039377464","display_name":"Renji Han","orcid":"https://orcid.org/0000-0001-5899-9943"},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Renji Han","raw_affiliation_strings":["School of Mathematics and Statistics, Central South University, Changsha 410083, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Central South University, Changsha 410083, P. R. China","institution_ids":["https://openalex.org/I139660479"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004518190","display_name":"Binxiang Dai","orcid":"https://orcid.org/0000-0003-2802-0743"},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Binxiang Dai","raw_affiliation_strings":["School of Mathematics and Statistics, Central South University, Changsha 410083, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Central South University, Changsha 410083, P. R. China","institution_ids":["https://openalex.org/I139660479"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5039377464"],"corresponding_institution_ids":["https://openalex.org/I139660479"],"apc_list":null,"apc_paid":null,"fwci":4.0055,"has_fulltext":false,"cited_by_count":46,"citation_normalized_percentile":{"value":0.93798158,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"27","issue":"06","first_page":"1750088","last_page":"1750088"},"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9980999827384949,"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/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.992900013923645,"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/diffusion","display_name":"Diffusion","score":0.5840126276016235},{"id":"https://openalex.org/keywords/zooplankton","display_name":"Zooplankton","score":0.5372436046600342},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.5089976787567139},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.4998500347137451},{"id":"https://openalex.org/keywords/phytoplankton","display_name":"Phytoplankton","score":0.4935077428817749},{"id":"https://openalex.org/keywords/amplitude","display_name":"Amplitude","score":0.4778125584125519},{"id":"https://openalex.org/keywords/instability","display_name":"Instability","score":0.47309282422065735},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.4688343405723572},{"id":"https://openalex.org/keywords/thermal-diffusivity","display_name":"Thermal diffusivity","score":0.4468294084072113},{"id":"https://openalex.org/keywords/ergodic-theory","display_name":"Ergodic theory","score":0.44127678871154785},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4384874403476715},{"id":"https://openalex.org/keywords/hopf-bifurcation","display_name":"Hopf bifurcation","score":0.43080857396125793},{"id":"https://openalex.org/keywords/biological-system","display_name":"Biological system","score":0.38251280784606934},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.34530556201934814},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.30115848779678345},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2310674786567688},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.22704243659973145},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.18836843967437744},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.18615010380744934},{"id":"https://openalex.org/keywords/ecology","display_name":"Ecology","score":0.1462879478931427},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14330309629440308},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.1190691888332367}],"concepts":[{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.5840126276016235},{"id":"https://openalex.org/C158836135","wikidata":"https://www.wikidata.org/wiki/Q842627","display_name":"Zooplankton","level":2,"score":0.5372436046600342},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5089976787567139},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.4998500347137451},{"id":"https://openalex.org/C2780892065","wikidata":"https://www.wikidata.org/wiki/Q184755","display_name":"Phytoplankton","level":3,"score":0.4935077428817749},{"id":"https://openalex.org/C180205008","wikidata":"https://www.wikidata.org/wiki/Q159190","display_name":"Amplitude","level":2,"score":0.4778125584125519},{"id":"https://openalex.org/C207821765","wikidata":"https://www.wikidata.org/wiki/Q405372","display_name":"Instability","level":2,"score":0.47309282422065735},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4688343405723572},{"id":"https://openalex.org/C37668627","wikidata":"https://www.wikidata.org/wiki/Q3381809","display_name":"Thermal diffusivity","level":2,"score":0.4468294084072113},{"id":"https://openalex.org/C122044880","wikidata":"https://www.wikidata.org/wiki/Q5498822","display_name":"Ergodic theory","level":2,"score":0.44127678871154785},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4384874403476715},{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.43080857396125793},{"id":"https://openalex.org/C186060115","wikidata":"https://www.wikidata.org/wiki/Q30336093","display_name":"Biological system","level":1,"score":0.38251280784606934},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.34530556201934814},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.30115848779678345},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2310674786567688},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.22704243659973145},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.18836843967437744},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.18615010380744934},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.1462879478931427},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14330309629440308},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.1190691888332367},{"id":"https://openalex.org/C142796444","wikidata":"https://www.wikidata.org/wiki/Q181394","display_name":"Nutrient","level":2,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127417500882","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127417500882","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":[{"score":0.7099999785423279,"id":"https://metadata.un.org/sdg/14","display_name":"Life below water"}],"awards":[{"id":"https://openalex.org/G4938649981","display_name":null,"funder_award_id":"11271371;51479215","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6851552610","display_name":null,"funder_award_id":"2013SQRL142ZD","funder_id":"https://openalex.org/F4320334973","funder_display_name":"Excellent Young Talents Fund Program of Higher Education Institutions of Anhui Province"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320334973","display_name":"Excellent Young Talents Fund Program of Higher Education Institutions of Anhui Province","ror":"https://ror.org/012m7k033"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W1518340778","https://openalex.org/W1593939215","https://openalex.org/W1969943429","https://openalex.org/W1973118029","https://openalex.org/W1977064482","https://openalex.org/W1980596056","https://openalex.org/W1984409514","https://openalex.org/W1985850326","https://openalex.org/W1988370584","https://openalex.org/W1997830348","https://openalex.org/W2003551594","https://openalex.org/W2011556092","https://openalex.org/W2011718564","https://openalex.org/W2012073479","https://openalex.org/W2014722655","https://openalex.org/W2014858379","https://openalex.org/W2016364330","https://openalex.org/W2019404680","https://openalex.org/W2022096522","https://openalex.org/W2040443526","https://openalex.org/W2051409628","https://openalex.org/W2052368913","https://openalex.org/W2052914066","https://openalex.org/W2055558450","https://openalex.org/W2061423359","https://openalex.org/W2074077770","https://openalex.org/W2076123824","https://openalex.org/W2078582015","https://openalex.org/W2089845038","https://openalex.org/W2089965269","https://openalex.org/W2101971786","https://openalex.org/W2103991009","https://openalex.org/W2113358203","https://openalex.org/W2138321095","https://openalex.org/W2206758789","https://openalex.org/W2266018905","https://openalex.org/W2335036936","https://openalex.org/W2467407750","https://openalex.org/W2481427767","https://openalex.org/W2491262456","https://openalex.org/W3104470002"],"related_works":["https://openalex.org/W2981311582","https://openalex.org/W2134233467","https://openalex.org/W3201695769","https://openalex.org/W2155439371","https://openalex.org/W3036695843","https://openalex.org/W2904071950","https://openalex.org/W2259986199","https://openalex.org/W4385436308","https://openalex.org/W3026272116","https://openalex.org/W3188981964"],"abstract_inverted_index":{"The":[0,19],"spatiotemporal":[1,98,121],"pattern":[2,171],"induced":[3],"by":[4],"cross-diffusion":[5,25,38],"of":[6,33,59,68,78,81,100,108,123,137,144,156,159,167],"a":[7,60],"toxic-phytoplankton\u2013zooplankton":[8],"model":[9],"with":[10],"nonmonotonic":[11],"functional":[12],"response":[13],"is":[14,26,94,103,114,173],"investigated":[15],"in":[16,56,105,130,134],"this":[17],"paper.":[18],"linear":[20],"stability":[21,66,77],"analysis":[22,67],"shows":[23],"that":[24,96],"the":[27,31,48,53,57,65,69,73,87,97,101,106,112,117,120,125,142,151,154],"key":[28],"mechanism":[29],"for":[30,52],"formation":[32],"spatial":[34],"patterns.":[35,83],"By":[36],"taking":[37],"rate":[39,158,166],"as":[40],"bifurcation":[41,50],"parameter,":[42],"we":[43,85],"derive":[44],"amplitude":[45,70],"equations":[46,71],"near":[47],"Turing":[49,82],"point":[51],"excited":[54],"modes":[55],"framework":[58],"weakly":[61],"nonlinear":[62],"theory,":[63],"and":[64,76,132,141,146,163],"interprets":[72],"structural":[74],"transitions":[75],"various":[79],"forms":[80],"Furthermore,":[84],"illustrate":[86],"theoretical":[88],"results":[89,133],"via":[90],"numerical":[91],"simulations.":[92],"It":[93],"shown":[95],"distribution":[99,122],"plankton":[102,126],"homogeneous":[104],"absence":[107],"cross-diffusion.":[109],"However,":[110],"when":[111],"cross-diffusivity":[113],"greater":[115],"than":[116],"critical":[118],"value,":[119],"all":[124],"species":[127,162,169],"becomes":[128],"inhomogeneous":[129],"spaces":[131],"different":[135],"kinds":[136],"patterns:":[138],"spot,":[139],"stripe,":[140],"mixture":[143],"spot":[145],"stripe":[147],"patterns":[148],"depending":[149],"on":[150,170],"cross-diffusivity.":[152],"Simultaneously,":[153],"impact":[155],"toxin-producing":[157],"toxic-phytoplankton":[160],"(TPP)":[161],"natural":[164],"death":[165],"zooplankton":[168],"selection":[172],"also":[174],"explored.":[175]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":10},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
