{"id":"https://openalex.org/W3110728547","doi":"https://doi.org/10.7498/aps.67.20171791","title":"Application of reaction diffusion model in Turing pattern and numerical simulation","display_name":"Application of reaction diffusion model in Turing pattern and numerical simulation","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W3110728547","doi":"https://doi.org/10.7498/aps.67.20171791","mag":"3110728547"},"language":"en","primary_location":{"id":"doi:10.7498/aps.67.20171791","doi":"https://doi.org/10.7498/aps.67.20171791","is_oa":true,"landing_page_url":"https://doi.org/10.7498/aps.67.20171791","pdf_url":null,"source":{"id":"https://openalex.org/S950076683","display_name":"Acta Physica Sinica","issn_l":"1000-3290","issn":["1000-3290"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1","ki-jl-1","norway-1","poland-20","russia-white-list-3"],"host_organization":"https://openalex.org/P4310319982","host_organization_name":"Science Press","host_organization_lineage":["https://openalex.org/P4310319982"],"host_organization_lineage_names":["Science Press"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Acta Physica Sinica","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.7498/aps.67.20171791","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015594917","display_name":"Rongpei Zhang","orcid":"https://orcid.org/0000-0003-1782-4922","observed_orcids":["https://orcid.org/0000-0003-1782-4922"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang Rong-Pei","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100422268","display_name":"Zhen Wang","orcid":"https://orcid.org/0000-0001-7188-5828","observed_orcids":["https://orcid.org/0000-0001-7188-5828","https://orcid.org/0009-0007-6288-4461"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang Zhen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100445217","display_name":"Yu Wang","orcid":"https://orcid.org/0000-0002-4788-8655","observed_orcids":["https://orcid.org/0000-0002-4788-8655"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang Yu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5096935824","display_name":"Han Zi-Jian","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Han Zi-Jian","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4623,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.57011251,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"67","issue":"5","first_page":"050503","last_page":"050503"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.961899995803833,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"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":0.961899995803833,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"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":0.01940000057220459,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.00419999985024333,"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/reaction-diffusion-systems","display_name":"reaction-diffusion systems","score":0.8220000267028809},{"id":"https://openalex.org/keywords/turing-patterns","display_name":"Turing patterns","score":0.6669999957084656},{"id":"https://openalex.org/keywords/turing-instability","display_name":"Turing instability","score":0.8679999709129333},{"id":"https://openalex.org/keywords/gierer-meinhardt-model","display_name":"Gierer-Meinhardt model","score":0.9520000219345093},{"id":"https://openalex.org/keywords/activator-inhibitor-systems","display_name":"activator-inhibitor systems","score":0.8519999980926514},{"id":"https://openalex.org/keywords/pattern-formation","display_name":"pattern formation","score":0.9229999780654907},{"id":"https://openalex.org/keywords/pseudospectral-method","display_name":"pseudospectral method","score":0.9079999923706055},{"id":"https://openalex.org/keywords/matrix-exponential","display_name":"matrix exponential","score":0.7860000133514404},{"id":"https://openalex.org/keywords/nonlinear-ordinary-differential-equations","display_name":"nonlinear ordinary differential equations","score":0.7279999852180481}],"concepts":[{"id":"https://openalex.org/C121231716","wikidata":"https://www.wikidata.org/wiki/Q901210","display_name":"Reaction\u2013diffusion system","level":2,"score":0.6399887800216675},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6214433312416077},{"id":"https://openalex.org/C207016750","wikidata":"https://www.wikidata.org/wiki/Q1955627","display_name":"Pattern formation","level":2,"score":0.4736422598361969},{"id":"https://openalex.org/C129785596","wikidata":"https://www.wikidata.org/wiki/Q619511","display_name":"Chebyshev polynomials","level":2,"score":0.42820703983306885},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.4189332127571106},{"id":"https://openalex.org/C181330731","wikidata":"https://www.wikidata.org/wiki/Q2068418","display_name":"Finite difference","level":2,"score":0.41798263788223267},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.41058871150016785},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.40718308091163635},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.38804876804351807},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3738548755645752},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.3558627665042877},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2424817979335785},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.7498/aps.67.20171791","doi":"https://doi.org/10.7498/aps.67.20171791","is_oa":true,"landing_page_url":"https://doi.org/10.7498/aps.67.20171791","pdf_url":null,"source":{"id":"https://openalex.org/S950076683","display_name":"Acta Physica Sinica","issn_l":"1000-3290","issn":["1000-3290"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1","ki-jl-1","norway-1","poland-20","russia-white-list-3"],"host_organization":"https://openalex.org/P4310319982","host_organization_name":"Science Press","host_organization_lineage":["https://openalex.org/P4310319982"],"host_organization_lineage_names":["Science Press"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Acta Physica Sinica","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.7498/aps.67.20171791","doi":"https://doi.org/10.7498/aps.67.20171791","is_oa":true,"landing_page_url":"https://doi.org/10.7498/aps.67.20171791","pdf_url":null,"source":{"id":"https://openalex.org/S950076683","display_name":"Acta Physica Sinica","issn_l":"1000-3290","issn":["1000-3290"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1","ki-jl-1","norway-1","poland-20","russia-white-list-3"],"host_organization":"https://openalex.org/P4310319982","host_organization_name":"Science Press","host_organization_lineage":["https://openalex.org/P4310319982"],"host_organization_lineage_names":["Science Press"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Acta Physica Sinica","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1556426368","https://openalex.org/W2019847677","https://openalex.org/W2052485881","https://openalex.org/W2057119480","https://openalex.org/W2073519923","https://openalex.org/W2089840306","https://openalex.org/W2126271587","https://openalex.org/W2159344399","https://openalex.org/W2160642865","https://openalex.org/W2238627384","https://openalex.org/W2242073678","https://openalex.org/W2275348164","https://openalex.org/W2317259993","https://openalex.org/W2321413920","https://openalex.org/W2501482867","https://openalex.org/W2571924096","https://openalex.org/W2613320246","https://openalex.org/W3114614005","https://openalex.org/W3117018461"],"related_works":["https://openalex.org/W2027244891","https://openalex.org/W2894882052","https://openalex.org/W2946734931","https://openalex.org/W4243176611","https://openalex.org/W2610015946","https://openalex.org/W2196708584","https://openalex.org/W4327740401","https://openalex.org/W4401443590","https://openalex.org/W4385733277","https://openalex.org/W4388715447"],"abstract_inverted_index":{"Turing":[0,14,119,125],"proposed":[1],"a":[2,24,135,176,285,309,349,393],"model":[3,42,50,68,84],"for":[4,288],"the":[5,35,51,65,75,78,82,88,96,101,113,118,124,131,150,163,168,171,182,185,190,201,205,218,227,231,235,240,246,252,261,270,278,289,293,324,330,334,338,342,362,365,369,397,402,417],"development":[6],"of":[7,54,77,81,100,112,123,137,170,179,184,204,264,333,341,364,399],"patterns":[8,400],"found":[9],"in":[10,12,70,200,230,304,323],"nature":[11],"1952.":[13],"instability":[15],"is":[16,43,60,85,93,198,256],"known":[17],"as":[18,321],"diffusion-driven":[19],"instability,":[20],"which":[21,158,313],"states":[22],"that":[23,95,389,401],"stable":[25],"spatially":[26],"homogeneous":[27],"equilibrium":[28,98],"may":[29],"lose":[30],"its":[31],"stability":[32],"due":[33],"to":[34,49,63,225,276],"unequal":[36],"spatial":[37,209,236,306,355],"diffusion":[38,90,114],"coefficients.":[39],"The":[40,57,121,413],"Gierer-Mainhardt":[41],"an":[44,193],"activator":[45],"and":[46,116,144,154,181,221,258,316,368,380,383],"inhibitor":[47],"system":[48,59,106,352,403],"generating":[52],"mechanism":[53,76],"biological":[55],"patterns.":[56],"reaction-diffusion":[58,206,232],"often":[61],"used":[62,199],"describe":[64],"pattern":[66,79,126],"formation":[67,80],"arising":[69],"biology.":[71],"In":[72,189,208],"this":[73],"paper,":[74],"Gierer-Meinhardt":[83],"deduced":[86],"from":[87,337],"reactive":[89],"model.":[91,132],"It":[92],"explained":[94],"steady":[97],"state":[99],"nonlinear":[102,241,279,343,351],"ordinary":[103,242,280],"differential":[104,243,248,281,291],"equation":[105],"will":[107],"be":[108],"unstable":[109],"after":[110],"adding":[111],"term":[115],"produce":[117],"pattern.":[120],"parameters":[122,405],"are":[127,134,314],"obtained":[128,250],"by":[129,251],"calculating":[130],"There":[133],"variety":[136],"numerical":[138,196,202,414],"methods":[139],"including":[140],"finite":[141,145,151,155],"difference":[142,152],"method":[143,153,165,255,275,298,328,359,367],"element":[146,156],"method.":[147],"Compared":[148],"with":[149,174,361],"method,":[157,374],"have":[159,318,392],"low":[160],"order":[161,173],"precision,":[162,377],"spectral":[164,247,253,290,366],"can":[166,391],"achieve":[167],"convergence":[169],"exponential":[172,301,311],"only":[175,347],"small":[177,319,381],"number":[178],"nodes":[180],"discretization":[183],"suitable":[186],"orthogonal":[187],"polynomials.":[188],"present":[191],"work,":[192],"efficient":[194],"high-precision":[195],"scheme":[197],"simulation":[203],"equations.":[207,244,282],"discretization,":[210,237],"we":[211,238,268],"construct":[212],"Chebyshev":[213,219],"differentiation":[214],"matrices":[215,224,312],"based":[216],"on":[217,396],"points":[220],"use":[222,260],"these":[223],"differentiate":[226],"second":[228],"derivative":[229],"equation.":[233],"After":[234],"obtain":[239],"Since":[245],"matrix":[249,300],"collocation":[254],"full":[257],"cannot":[259],"fast":[262],"solution":[263],"algebraic":[265],"linear":[266,335],"equations,":[267],"choose":[269],"compact":[271,286,294,370],"implicit":[272,295,339,371],"integration":[273,296,372],"factor":[274,297,373],"solve":[277,348],"By":[283],"introducing":[284],"representation":[287],"matrix,":[292],"uses":[299],"operations":[302],"sequentially":[303],"every":[305],"direction.":[307],"As":[308],"result,":[310],"calculated":[315],"stored":[317],"sizes,":[320],"those":[322],"one-dimensional":[325],"problem.":[326],"This":[327,358],"decouples":[329],"exact":[331],"evaluation":[332],"part":[336],"treatment":[340],"reaction":[344],"terms.":[345],"We":[346],"local":[350],"at":[353],"each":[354],"grid":[356],"point.":[357],"combines":[360],"advantages":[363],"i.e.,":[375],"high":[376],"good":[378],"stability,":[379],"storage":[382],"so":[384],"on.":[385],"Numerical":[386],"simulations":[387],"show":[388],"it":[390],"great":[394],"influence":[395],"generation":[398],"control":[404],"take":[406],"different":[407],"values":[408],"under":[409],"otherwise":[410],"identical":[411],"conditions.":[412],"results":[415],"verify":[416],"theoretical":[418],"results.":[419]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1}],"updated_date":"2026-10-13T10:08:12.033832","created_date":"2020-12-21T00:00:00"}