{"id":"https://openalex.org/W3042672910","doi":"https://doi.org/10.1142/s0218127420501217","title":"Study on Turing Patterns of Gray\u2013Scott Model via Amplitude Equation","display_name":"Study on Turing Patterns of Gray\u2013Scott Model via Amplitude Equation","publication_year":2020,"publication_date":"2020-06-30","ids":{"openalex":"https://openalex.org/W3042672910","doi":"https://doi.org/10.1142/s0218127420501217","mag":"3042672910"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127420501217","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127420501217","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/A5102192945","display_name":"Wen-Xian Xie","orcid":null},"institutions":[{"id":"https://openalex.org/I17145004","display_name":"Northwestern Polytechnical University","ror":"https://ror.org/01y0j0j86","country_code":"CN","type":"education","lineage":["https://openalex.org/I17145004"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wen-Xian Xie","raw_affiliation_strings":["Department of Applied Mathematics, Northwestern Polytechnical University, Xi\u2019an, Shaanxi 710129, P. R. China","Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, Shaanxi 710129, P. R. China"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Northwestern Polytechnical University, Xi\u2019an, Shaanxi 710129, P. R. China","institution_ids":["https://openalex.org/I17145004"]},{"raw_affiliation_string":"Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, Shaanxi 710129, P. R. China","institution_ids":["https://openalex.org/I17145004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066533789","display_name":"Shuping Cao","orcid":null},"institutions":[{"id":"https://openalex.org/I17145004","display_name":"Northwestern Polytechnical University","ror":"https://ror.org/01y0j0j86","country_code":"CN","type":"education","lineage":["https://openalex.org/I17145004"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Shu-Ping Cao","raw_affiliation_strings":["Department of Applied Mathematics, Northwestern Polytechnical University, Xi\u2019an, Shaanxi 710129, P. R. China","Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, Shaanxi 710129, P. R. China"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Northwestern Polytechnical University, Xi\u2019an, Shaanxi 710129, P. R. China","institution_ids":["https://openalex.org/I17145004"]},{"raw_affiliation_string":"Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, Shaanxi 710129, P. R. China","institution_ids":["https://openalex.org/I17145004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032874350","display_name":"Li Cai","orcid":"https://orcid.org/0000-0002-2031-2015"},"institutions":[{"id":"https://openalex.org/I17145004","display_name":"Northwestern Polytechnical University","ror":"https://ror.org/01y0j0j86","country_code":"CN","type":"education","lineage":["https://openalex.org/I17145004"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Li Cai","raw_affiliation_strings":["NPU-UoG International Cooperative Lab for Computation and Application in Cardiology, Northwestern Polytechnical University, Xi\u2019an, Shaanxi 710129, P. R. China","NPU-UoG International Cooperative Lab for Computation and Application in Cardiology, Northwestern Polytechnical University, Xi'an, Shaanxi 710129, P. R. China"],"affiliations":[{"raw_affiliation_string":"NPU-UoG International Cooperative Lab for Computation and Application in Cardiology, Northwestern Polytechnical University, Xi\u2019an, Shaanxi 710129, P. R. China","institution_ids":["https://openalex.org/I17145004"]},{"raw_affiliation_string":"NPU-UoG International Cooperative Lab for Computation and Application in Cardiology, Northwestern Polytechnical University, Xi'an, Shaanxi 710129, P. R. China","institution_ids":["https://openalex.org/I17145004"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100712577","display_name":"Xiaoxuan Zhang","orcid":"https://orcid.org/0000-0003-1976-680X"},"institutions":[{"id":"https://openalex.org/I17145004","display_name":"Northwestern Polytechnical University","ror":"https://ror.org/01y0j0j86","country_code":"CN","type":"education","lineage":["https://openalex.org/I17145004"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiao-Xuan Zhang","raw_affiliation_strings":["Department of Applied Mathematics, Northwestern Polytechnical University, Xi\u2019an, Shaanxi 710129, P. R. China","Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, Shaanxi 710129, P. R. China"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Northwestern Polytechnical University, Xi\u2019an, Shaanxi 710129, P. R. China","institution_ids":["https://openalex.org/I17145004"]},{"raw_affiliation_string":"Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, Shaanxi 710129, P. R. China","institution_ids":["https://openalex.org/I17145004"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5066533789"],"corresponding_institution_ids":["https://openalex.org/I17145004"],"apc_list":null,"apc_paid":null,"fwci":0.4837,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.67711629,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"30","issue":"08","first_page":"2050121","last_page":"2050121"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9998999834060669,"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/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9991000294685364,"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/T13377","display_name":"Ecosystem dynamics and resilience","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/2306","display_name":"Global and Planetary Change"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/turing","display_name":"Turing","score":0.736821174621582},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.5162289142608643},{"id":"https://openalex.org/keywords/amplitude","display_name":"Amplitude","score":0.5038163065910339},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.48640871047973633},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4412071704864502},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.4367653727531433},{"id":"https://openalex.org/keywords/position","display_name":"Position (finance)","score":0.4142940640449524},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.36990147829055786},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.36681342124938965},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.25999587774276733},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.25305676460266113},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.07540658116340637},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.0651792585849762}],"concepts":[{"id":"https://openalex.org/C9870796","wikidata":"https://www.wikidata.org/wiki/Q490481","display_name":"Turing","level":2,"score":0.736821174621582},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.5162289142608643},{"id":"https://openalex.org/C180205008","wikidata":"https://www.wikidata.org/wiki/Q159190","display_name":"Amplitude","level":2,"score":0.5038163065910339},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.48640871047973633},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4412071704864502},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.4367653727531433},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.4142940640449524},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.36990147829055786},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.36681342124938965},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.25999587774276733},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.25305676460266113},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.07540658116340637},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0651792585849762},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127420501217","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127420501217","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":[{"id":"https://openalex.org/G1913634808","display_name":null,"funder_award_id":"11871399","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"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W803162307","https://openalex.org/W1980661496","https://openalex.org/W1982696897","https://openalex.org/W1989999409","https://openalex.org/W1999747351","https://openalex.org/W2002872087","https://openalex.org/W2006640177","https://openalex.org/W2016935008","https://openalex.org/W2018942014","https://openalex.org/W2019177912","https://openalex.org/W2036315044","https://openalex.org/W2046671196","https://openalex.org/W2056977870","https://openalex.org/W2060007406","https://openalex.org/W2074053825","https://openalex.org/W2079523665","https://openalex.org/W2080580900","https://openalex.org/W2082227405","https://openalex.org/W2089965269","https://openalex.org/W2093457643","https://openalex.org/W2153575924","https://openalex.org/W2161045785","https://openalex.org/W2225919032","https://openalex.org/W2342910085","https://openalex.org/W2540417229","https://openalex.org/W2577347286","https://openalex.org/W2731338476","https://openalex.org/W2770299407","https://openalex.org/W2889208097","https://openalex.org/W2892666260","https://openalex.org/W2922136954"],"related_works":["https://openalex.org/W577185743","https://openalex.org/W2004357175","https://openalex.org/W1600683501","https://openalex.org/W1974134410","https://openalex.org/W4302028307","https://openalex.org/W2064502186","https://openalex.org/W1990192565","https://openalex.org/W1495683925","https://openalex.org/W4212896882","https://openalex.org/W2107148245"],"abstract_inverted_index":{"In":[0],"this":[1,32,65,207],"paper,":[2],"the":[3,13,26,41,44,49,54,61,70,76,81,84,93,97,104,111,119,122,128,132,138,147,151,156,160,165,171,177,184,187,192,203,209,217,226,229,236,241,245],"amplitude":[4,85],"equations":[5],"of":[6,28,43,64,69,83,96,110,114,121,134,150,159,167,170,186,194,216,228,235,244],"a":[7,39],"Gray\u2013Scott":[8],"model":[9,33],"without":[10],"(or":[11],"with)":[12],"feedback":[14,139,178,237],"time":[15,50,140,175,179,238],"delay":[16,51,141,180,239],"are":[17,125,221],"derived":[18],"based":[19],"on":[20,53,146,240],"weakly":[21],"nonlinear":[22],"method,":[23],"by":[24,103],"which":[25,223],"selection":[27],"Turing":[29,55,98,135,152,161,188,195,211,246],"patterns":[30,99,189,196,212],"for":[31,206],"can":[34,57,182],"be":[35,58],"theoretically":[36],"determined.":[37],"As":[38],"result,":[40],"effects":[42],"diffusion":[45,71,105,116,172,218,230],"coefficient":[46,106,117,219,231],"ratio":[47,107,169,232],"and":[48,108,190,233],"factor":[52,142,181],"pattern":[56],"investigated":[59],"as":[60,75,127],"main":[62],"purpose":[63],"paper.":[66],"If":[67],"one":[68],"coefficients":[72],"is":[73,90,100],"chosen":[74],"bifurcation":[77,95,149,243],"control":[78],"parameter":[79],"in":[80,131,164],"procedure":[82],"equation":[86],"at":[87,197],"first,":[88],"it":[89],"proved":[91],"that":[92],"first-order":[94,148,242],"only":[101],"determined":[102],"independent":[109],"concrete":[112],"value":[113],"each":[115,198],"once":[118],"parameters":[120],"reaction":[123],"terms":[124],"fixed":[126],"appropriate":[129],"constants":[130],"regions":[133],"patterns.":[136,247],"Furthermore,":[137],"has":[143],"no":[144],"effect":[145],"patterns,":[153,162],"but":[154],"affects":[155],"morphological":[157],"characteristics":[158],"especially":[163],"case":[166],"large":[168],"coefficients.":[173],"With":[174],"increasing,":[176],"postpone":[183],"formation":[185],"cause":[191],"oscillations":[193],"spatial":[199],"position.":[200],"By":[201],"implementing":[202],"numerical":[204],"calculations":[205],"model,":[208],"various":[210],"with":[213],"different":[214],"values":[215],"ratios":[220],"presented,":[222],"really":[224],"verify":[225],"dependence":[227],"independence":[234]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}
