{"id":"https://openalex.org/W2523066125","doi":"https://doi.org/10.1142/s0218127416501674","title":"Hopf Bifurcation and Delay-Induced Turing Instability in a Diffusive <i>lac</i> Operon Model","display_name":"Hopf Bifurcation and Delay-Induced Turing Instability in a Diffusive <i>lac</i> Operon Model","publication_year":2016,"publication_date":"2016-09-01","ids":{"openalex":"https://openalex.org/W2523066125","doi":"https://doi.org/10.1142/s0218127416501674","mag":"2523066125"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127416501674","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127416501674","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/A5078462358","display_name":"Xin Cao","orcid":"https://orcid.org/0000-0001-6920-2717"},"institutions":[{"id":"https://openalex.org/I116953780","display_name":"Tongji University","ror":"https://ror.org/03rc6as71","country_code":"CN","type":"education","lineage":["https://openalex.org/I116953780"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xin Cao","raw_affiliation_strings":["Department of Mathematics, Tongji University, Shanghai 200092, P. R. China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Tongji University, Shanghai 200092, P. R. China","institution_ids":["https://openalex.org/I116953780"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026187828","display_name":"Yongli Song","orcid":"https://orcid.org/0000-0002-2209-2458"},"institutions":[{"id":"https://openalex.org/I163151501","display_name":"Hangzhou Normal University","ror":"https://ror.org/014v1mr15","country_code":"CN","type":"education","lineage":["https://openalex.org/I163151501"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yongli Song","raw_affiliation_strings":["Department of Mathematics, Hangzhou Normal University, Hangzhou 311121, P. R. China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Hangzhou Normal University, Hangzhou 311121, P. R. China","institution_ids":["https://openalex.org/I163151501"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5086628608","display_name":"Tonghua Zhang","orcid":"https://orcid.org/0000-0003-0510-1428"},"institutions":[{"id":"https://openalex.org/I57093077","display_name":"Swinburne University of Technology","ror":"https://ror.org/031rekg67","country_code":"AU","type":"education","lineage":["https://openalex.org/I57093077"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Tonghua Zhang","raw_affiliation_strings":["Department of Mathematics, Swinburne University of Technology, Victoria 3122, Australia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Swinburne University of Technology, Victoria 3122, Australia","institution_ids":["https://openalex.org/I57093077"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5078462358"],"corresponding_institution_ids":["https://openalex.org/I116953780"],"apc_list":null,"apc_paid":null,"fwci":2.3163,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.89693635,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"26","issue":"10","first_page":"1650167","last_page":"1650167"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9988999962806702,"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/T10621","display_name":"Gene Regulatory Network Analysis","score":0.9934999942779541,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"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/hopf-bifurcation","display_name":"Hopf bifurcation","score":0.6317600607872009},{"id":"https://openalex.org/keywords/instability","display_name":"Instability","score":0.5835329294204712},{"id":"https://openalex.org/keywords/dynamics","display_name":"Dynamics (music)","score":0.5740188956260681},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.5300310254096985},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.47959935665130615},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4791092872619629},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.4729209542274475},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.47243863344192505},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4015406668186188},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.29960644245147705},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.1946772336959839},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.07230904698371887},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.06744980812072754}],"concepts":[{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.6317600607872009},{"id":"https://openalex.org/C207821765","wikidata":"https://www.wikidata.org/wiki/Q405372","display_name":"Instability","level":2,"score":0.5835329294204712},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.5740188956260681},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5300310254096985},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.47959935665130615},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4791092872619629},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4729209542274475},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.47243863344192505},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4015406668186188},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.29960644245147705},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.1946772336959839},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.07230904698371887},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.06744980812072754},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218127416501674","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127416501674","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"},{"id":"pmh:oai:researchbank.swinburne.edu.au:a8677111-8e1a-40ef-a9da-9c22d2ef7e24/1","is_oa":false,"landing_page_url":"http://hdl.handle.net/1959.3/433392","pdf_url":null,"source":{"id":"https://openalex.org/S4306401157","display_name":"Swinburne Research Bank (Swinburne University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I57093077","host_organization_name":"Swinburne University of Technology","host_organization_lineage":["https://openalex.org/I57093077"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International Journal of Bifurcation and Chaos in Applied Sciences and Engineering , Vol. 26, no. 10 (Sep 2016), article no. 1650167","raw_type":""}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8940736242","display_name":null,"funder_award_id":"11571257","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":36,"referenced_works":["https://openalex.org/W1603340857","https://openalex.org/W1605753492","https://openalex.org/W1645305843","https://openalex.org/W1822833310","https://openalex.org/W1929947366","https://openalex.org/W1964749479","https://openalex.org/W1965738187","https://openalex.org/W1966423352","https://openalex.org/W1971327350","https://openalex.org/W1972144300","https://openalex.org/W1983550039","https://openalex.org/W1986872576","https://openalex.org/W1987790493","https://openalex.org/W1994094413","https://openalex.org/W2000035140","https://openalex.org/W2001888401","https://openalex.org/W2003836735","https://openalex.org/W2009564087","https://openalex.org/W2024882852","https://openalex.org/W2030945597","https://openalex.org/W2040802713","https://openalex.org/W2051312368","https://openalex.org/W2086222060","https://openalex.org/W2093457643","https://openalex.org/W2095248288","https://openalex.org/W2102265921","https://openalex.org/W2119729354","https://openalex.org/W2123100388","https://openalex.org/W2126750481","https://openalex.org/W2132828256","https://openalex.org/W2167829186","https://openalex.org/W2169242133","https://openalex.org/W2169316089","https://openalex.org/W2301716655","https://openalex.org/W4231550443","https://openalex.org/W4236463097"],"related_works":["https://openalex.org/W3128490882","https://openalex.org/W2001548992","https://openalex.org/W2114166374","https://openalex.org/W2735971053","https://openalex.org/W2065431515","https://openalex.org/W2509557608","https://openalex.org/W2898039612","https://openalex.org/W2018290803","https://openalex.org/W1913209438","https://openalex.org/W2143912965"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"investigate":[4],"the":[5,21,27,31,45,51,84],"dynamics":[6,59],"of":[7],"a":[8],"[Formula:":[9],"see":[10],"text]":[11],"operon":[12],"model":[13],"with":[14,94],"delayed":[15],"feedback":[16],"and":[17,101],"diffusion":[18],"effect.":[19],"If":[20],"system":[22,85],"is":[23,29,34,48],"without":[24],"delay":[25,28,47,67],"or":[26],"small,":[30],"positive":[32],"equilibrium":[33,52],"stable":[35],"so":[36,55],"that":[37,56,65],"there":[38],"are":[39],"no":[40],"spatial":[41,89],"patterns":[42],"formed;":[43],"while":[44],"time":[46,66],"large":[49],"enough":[50],"becomes":[53],"unstable":[54],"rich":[57],"spatiotemporal":[58],"may":[60,86],"occur.":[61],"We":[62],"have":[63,87],"found":[64],"can":[68],"not":[69],"only":[70],"incur":[71],"temporal":[72],"oscillations":[73],"but":[74],"also":[75],"induce":[76],"imbalance":[77],"in":[78],"space.":[79],"With":[80],"different":[81,88],"initial":[82],"values,":[83],"patterns,":[90],"for":[91],"instance,":[92],"spirals":[93],"one":[95],"head,":[96],"four":[97],"heads,":[98,100],"nine":[99],"even":[102],"microspirals.":[103]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
