{"id":"https://openalex.org/W1988004926","doi":"https://doi.org/10.1142/s0218127413501629","title":"TURING PATTERN FORMATION IN A TWO-SPECIES NEGATIVE FEEDBACK SYSTEM WITH CROSS-DIFFUSION","display_name":"TURING PATTERN FORMATION IN A TWO-SPECIES NEGATIVE FEEDBACK SYSTEM WITH CROSS-DIFFUSION","publication_year":2013,"publication_date":"2013-09-01","ids":{"openalex":"https://openalex.org/W1988004926","doi":"https://doi.org/10.1142/s0218127413501629","mag":"1988004926"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127413501629","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127413501629","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/A5101709100","display_name":"Xiyan Yang","orcid":"https://orcid.org/0000-0002-5166-1701"},"institutions":[{"id":"https://openalex.org/I157773358","display_name":"Sun Yat-sen University","ror":"https://ror.org/0064kty71","country_code":"CN","type":"education","lineage":["https://openalex.org/I157773358"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"XIYAN YANG","raw_affiliation_strings":["School of Mathematics and Computational Science, Sun Yat-Sen University, Guangzhou 510275, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Computational Science, Sun Yat-Sen University, Guangzhou 510275, P. R. China","institution_ids":["https://openalex.org/I157773358"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109591222","display_name":"Zhanjiang Yuan","orcid":"https://orcid.org/0009-0004-7344-4814"},"institutions":[{"id":"https://openalex.org/I157773358","display_name":"Sun Yat-sen University","ror":"https://ror.org/0064kty71","country_code":"CN","type":"education","lineage":["https://openalex.org/I157773358"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"ZHANJIANG YUAN","raw_affiliation_strings":["School of Mathematics and Computational Science, Sun Yat-Sen University, Guangzhou 510275, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Computational Science, Sun Yat-Sen University, Guangzhou 510275, P. R. China","institution_ids":["https://openalex.org/I157773358"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110896615","display_name":"Tianshou Zhou","orcid":"https://orcid.org/0000-0003-3638-8679"},"institutions":[{"id":"https://openalex.org/I157773358","display_name":"Sun Yat-sen University","ror":"https://ror.org/0064kty71","country_code":"CN","type":"education","lineage":["https://openalex.org/I157773358"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"TIANSHOU ZHOU","raw_affiliation_strings":["School of Mathematics and Computational Science, Sun Yat-Sen University, Guangzhou 510275, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Computational Science, Sun Yat-Sen University, Guangzhou 510275, P. R. China","institution_ids":["https://openalex.org/I157773358"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5101709100"],"corresponding_institution_ids":["https://openalex.org/I157773358"],"apc_list":null,"apc_paid":null,"fwci":0.7542,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.74286495,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"23","issue":"09","first_page":"1350162","last_page":"1350162"},"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":0.9976000189781189,"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":0.9962000250816345,"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/turing","display_name":"Turing","score":0.8044424057006836},{"id":"https://openalex.org/keywords/pattern-formation","display_name":"Pattern formation","score":0.6821631789207458},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.5992483496665955},{"id":"https://openalex.org/keywords/spatiotemporal-pattern","display_name":"Spatiotemporal pattern","score":0.4533088803291321},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.4268467128276825},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.36121487617492676},{"id":"https://openalex.org/keywords/biological-system","display_name":"Biological system","score":0.3220127820968628},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.29499149322509766},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.18269377946853638},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.08559006452560425}],"concepts":[{"id":"https://openalex.org/C9870796","wikidata":"https://www.wikidata.org/wiki/Q490481","display_name":"Turing","level":2,"score":0.8044424057006836},{"id":"https://openalex.org/C207016750","wikidata":"https://www.wikidata.org/wiki/Q1955627","display_name":"Pattern formation","level":2,"score":0.6821631789207458},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.5992483496665955},{"id":"https://openalex.org/C2779108282","wikidata":"https://www.wikidata.org/wiki/Q22908968","display_name":"Spatiotemporal pattern","level":2,"score":0.4533088803291321},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4268467128276825},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36121487617492676},{"id":"https://openalex.org/C186060115","wikidata":"https://www.wikidata.org/wiki/Q30336093","display_name":"Biological system","level":1,"score":0.3220127820968628},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.29499149322509766},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.18269377946853638},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.08559006452560425},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127413501629","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127413501629","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/15","display_name":"Life in Land"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":57,"referenced_works":["https://openalex.org/W1641228030","https://openalex.org/W1964625848","https://openalex.org/W1965833176","https://openalex.org/W1971379540","https://openalex.org/W1977760850","https://openalex.org/W1979450477","https://openalex.org/W1980661496","https://openalex.org/W1982088462","https://openalex.org/W1990000710","https://openalex.org/W1992963104","https://openalex.org/W1993592538","https://openalex.org/W2000920414","https://openalex.org/W2001168415","https://openalex.org/W2006640177","https://openalex.org/W2013895832","https://openalex.org/W2015029297","https://openalex.org/W2016095496","https://openalex.org/W2017370428","https://openalex.org/W2017463008","https://openalex.org/W2017659568","https://openalex.org/W2019475305","https://openalex.org/W2019629909","https://openalex.org/W2024453017","https://openalex.org/W2033455197","https://openalex.org/W2037486322","https://openalex.org/W2040570894","https://openalex.org/W2041046749","https://openalex.org/W2047506587","https://openalex.org/W2047578520","https://openalex.org/W2047703408","https://openalex.org/W2050057967","https://openalex.org/W2060243607","https://openalex.org/W2061425021","https://openalex.org/W2064716281","https://openalex.org/W2070102480","https://openalex.org/W2072700524","https://openalex.org/W2073213523","https://openalex.org/W2076123824","https://openalex.org/W2086126894","https://openalex.org/W2087254342","https://openalex.org/W2087497076","https://openalex.org/W2089840306","https://openalex.org/W2092424552","https://openalex.org/W2102687131","https://openalex.org/W2106311948","https://openalex.org/W2117450472","https://openalex.org/W2120466844","https://openalex.org/W2123584715","https://openalex.org/W2127071442","https://openalex.org/W2132688627","https://openalex.org/W2141964940","https://openalex.org/W2142507929","https://openalex.org/W2143862413","https://openalex.org/W2154861644","https://openalex.org/W2158537201","https://openalex.org/W2331173871","https://openalex.org/W4254540798"],"related_works":["https://openalex.org/W2132847744","https://openalex.org/W4389224764","https://openalex.org/W2015141095","https://openalex.org/W4361273936","https://openalex.org/W2101539302","https://openalex.org/W3214411012","https://openalex.org/W4313528897","https://openalex.org/W2099851527","https://openalex.org/W3208589169","https://openalex.org/W1988004926"],"abstract_inverted_index":{"Pattern":[0],"formation":[1,95,135],"is":[2,32,114],"a":[3,54,137,148],"ubiquitous":[4],"phenomenon":[5],"in":[6,44,48,99,103,136],"the":[7,27,30,38,86,92,104,107,115,121,130],"natural":[8],"world.":[9],"Previous":[10],"studies":[11],"showed":[12],"that":[13,36,82],"for":[14,73],"an":[15],"activator\u2013inhibitor":[16],"system":[17,59,122],"without":[18],"cross-diffusion,":[19],"spatial":[20],"patterns":[21],"can":[22,89],"be":[23],"formed":[24],"only":[25,118],"when":[26],"diffusion":[28,109,144],"of":[29,37,66,85,97,106,117,132,139],"inhibitor":[31],"significantly":[33],"faster":[34],"than":[35],"activator.":[39],"However,":[40,102],"cross-diffusion":[41,116],"exists":[42],"extensively":[43],"real":[45],"systems,":[46,141],"especially":[47],"biological":[49],"systems.":[50],"Here,":[51],"we":[52,69],"study":[53],"prototypic":[55],"two-species":[56],"negative":[57],"feedback":[58],"with":[60],"cross-diffusion.":[61],"By":[62],"performing":[63],"stability":[64],"analysis":[65],"equilibrium":[67],"state,":[68],"find":[70],"sufficient":[71],"conditions":[72],"Turing":[74,93,125,133],"instability.":[75],"Both":[76],"analytical":[77],"and":[78],"numerical":[79],"results":[80,128],"demonstrate":[81],"mutual":[83,108,143],"diffusions":[84],"two":[87],"species":[88,146],"lead":[90],"to":[91],"pattern":[94,134],"regardless":[96],"differences":[98],"self-diffusion":[100],"coefficients.":[101],"absence":[105],"or":[110],"even":[111],"if":[112],"there":[113],"one":[119],"species,":[120],"cannot":[123],"exhibit":[124],"patterns.":[126],"Our":[127],"reveal":[129],"mechanism":[131],"class":[138],"reaction\u2013diffusion":[140],"where":[142],"between":[145],"plays":[147],"key":[149],"role.":[150]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
