{"id":"https://openalex.org/W4402609128","doi":"https://doi.org/10.1142/s0218127424501621","title":"Turing\u2013Hopf Bifurcation Coinduced by Diffusion and Delay in Gierer\u2013Meinhardt Systems","display_name":"Turing\u2013Hopf Bifurcation Coinduced by Diffusion and Delay in Gierer\u2013Meinhardt Systems","publication_year":2024,"publication_date":"2024-09-18","ids":{"openalex":"https://openalex.org/W4402609128","doi":"https://doi.org/10.1142/s0218127424501621"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127424501621","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127424501621","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/A5057562219","display_name":"Xiangyi Ma","orcid":"https://orcid.org/0009-0001-3313-1854"},"institutions":[{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xiangyi Ma","raw_affiliation_strings":["School of Mathematical Sciences, Beihang University, Beijing 100191, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Beihang University, Beijing 100191, P. R. China","institution_ids":["https://openalex.org/I82880672"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100632262","display_name":"Jinliang Wang","orcid":"https://orcid.org/0000-0002-8696-5182"},"institutions":[{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jinliang Wang","raw_affiliation_strings":["School of Mathematical Sciences, Beihang University, Beijing 100191, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Beihang University, Beijing 100191, P. R. China","institution_ids":["https://openalex.org/I82880672"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5106414781","display_name":"Yongshuo Zhu","orcid":null},"institutions":[{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yanhua Zhu","raw_affiliation_strings":["School of Mathematical Sciences, Beihang University, Beijing 100191, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Beihang University, Beijing 100191, P. R. China","institution_ids":["https://openalex.org/I82880672"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103130709","display_name":"Ziwei Wang","orcid":"https://orcid.org/0009-0008-6684-7024"},"institutions":[{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ziwei Wang","raw_affiliation_strings":["School of Instrumentation and Optoelectronic Engineering, Beihang University, Beijing 100191, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Instrumentation and Optoelectronic Engineering, Beihang University, Beijing 100191, P. R. China","institution_ids":["https://openalex.org/I82880672"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100355560","display_name":"Ying Sun","orcid":"https://orcid.org/0000-0003-0555-1293"},"institutions":[{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ying Sun","raw_affiliation_strings":["School of Mathematical Sciences, Beihang University, Beijing 100191, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Beihang University, Beijing 100191, P. R. China","institution_ids":["https://openalex.org/I82880672"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5057562219"],"corresponding_institution_ids":["https://openalex.org/I82880672"],"apc_list":null,"apc_paid":null,"fwci":0.7326,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.72773565,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"34","issue":"13","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9811999797821045,"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":0.9811999797821045,"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/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9175000190734863,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/hopf-bifurcation","display_name":"Hopf bifurcation","score":0.7478296756744385},{"id":"https://openalex.org/keywords/biological-applications-of-bifurcation-theory","display_name":"Biological applications of bifurcation theory","score":0.6581420302391052},{"id":"https://openalex.org/keywords/turing","display_name":"Turing","score":0.6023622155189514},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5564188957214355},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.5519251823425293},{"id":"https://openalex.org/keywords/pitchfork-bifurcation","display_name":"Pitchfork bifurcation","score":0.5303509831428528},{"id":"https://openalex.org/keywords/bogdanov\u2013takens-bifurcation","display_name":"Bogdanov\u2013Takens bifurcation","score":0.49280479550361633},{"id":"https://openalex.org/keywords/saddle-node-bifurcation","display_name":"Saddle-node bifurcation","score":0.4664003252983093},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3506810665130615},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.34986740350723267},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2950904369354248},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.24413400888442993},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.11589208245277405},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.08665120601654053}],"concepts":[{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.7478296756744385},{"id":"https://openalex.org/C174914120","wikidata":"https://www.wikidata.org/wiki/Q4914973","display_name":"Biological applications of bifurcation theory","level":5,"score":0.6581420302391052},{"id":"https://openalex.org/C9870796","wikidata":"https://www.wikidata.org/wiki/Q490481","display_name":"Turing","level":2,"score":0.6023622155189514},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5564188957214355},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.5519251823425293},{"id":"https://openalex.org/C155092403","wikidata":"https://www.wikidata.org/wiki/Q1785924","display_name":"Pitchfork bifurcation","level":5,"score":0.5303509831428528},{"id":"https://openalex.org/C22257346","wikidata":"https://www.wikidata.org/wiki/Q4937510","display_name":"Bogdanov\u2013Takens bifurcation","level":5,"score":0.49280479550361633},{"id":"https://openalex.org/C101225446","wikidata":"https://www.wikidata.org/wiki/Q740190","display_name":"Saddle-node bifurcation","level":4,"score":0.4664003252983093},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3506810665130615},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.34986740350723267},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2950904369354248},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.24413400888442993},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.11589208245277405},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.08665120601654053},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127424501621","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127424501621","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/G4123792083","display_name":null,"funder_award_id":"10971009","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6382656475","display_name":null,"funder_award_id":"11771033","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W1980661496","https://openalex.org/W1992267419","https://openalex.org/W2009354787","https://openalex.org/W2063032390","https://openalex.org/W2089840306","https://openalex.org/W2147862089","https://openalex.org/W2153575924","https://openalex.org/W2168179868","https://openalex.org/W2240649680","https://openalex.org/W2574151704","https://openalex.org/W2765856888","https://openalex.org/W2801141183","https://openalex.org/W2947165724","https://openalex.org/W2989866992","https://openalex.org/W3008413880","https://openalex.org/W3173921470","https://openalex.org/W3185709888","https://openalex.org/W4220661805","https://openalex.org/W4220776914","https://openalex.org/W4231204877","https://openalex.org/W4292416420","https://openalex.org/W4296534458","https://openalex.org/W4319921199","https://openalex.org/W4323364953","https://openalex.org/W4367046426"],"related_works":["https://openalex.org/W2356715721","https://openalex.org/W2546487931","https://openalex.org/W2025138898","https://openalex.org/W3020506472","https://openalex.org/W2356226573","https://openalex.org/W2110197045","https://openalex.org/W4365441268","https://openalex.org/W4388961837","https://openalex.org/W2325048728","https://openalex.org/W4245057904"],"abstract_inverted_index":{"This":[0],"paper":[1],"investigates":[2],"the":[3,13,33,42,46,49,54,86,99],"impact":[4],"of":[5,16,19,35,45,101],"gene":[6],"expression":[7],"time":[8],"delay":[9],"and":[10,29,38,65,74],"diffusion":[11],"on":[12],"dynamic":[14],"behavior":[15],"a":[17],"class":[18],"Gierer\u2013Meinhardt":[20],"systems":[21,87],"under":[22,95],"Neumann":[23],"boundary":[24],"conditions.":[25],"It":[26],"provides":[27],"necessary":[28],"sufficient":[30],"conditions":[31],"for":[32],"emergence":[34,100],"Hopf,":[36],"Turing,":[37],"Turing\u2013Hopf":[39,47,102],"bifurcations.":[40],"Utilizing":[41],"normal":[43],"form":[44],"bifurcation,":[48],"spatiotemporal":[50],"dynamics":[51],"close":[52],"to":[53],"bifurcation":[55],"point":[56],"are":[57,106],"categorized":[58],"into":[59],"six":[60],"types,":[61],"encompassing":[62],"spatially":[63,72,91],"inhomogeneous":[64,75,92],"homogeneous":[66,73],"periodic":[67,93],"solutions,":[68],"as":[69,71],"well":[70],"steady":[76],"states,":[77],"along":[78],"with":[79],"their":[80],"transitions.":[81],"Notably,":[82],"it\u2019s":[83],"observed":[84],"that":[85],"may":[88],"lack":[89],"stable":[90],"solutions":[94],"specific":[96],"parameters,":[97],"despite":[98],"bifurcation.":[103],"These":[104],"findings":[105],"supported":[107],"by":[108],"numerical":[109],"simulations.":[110]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2025-12-21T01:58:51.020947","created_date":"2025-10-10T00:00:00"}