{"id":"https://openalex.org/W7127621100","doi":"https://doi.org/10.3390/math14030563","title":"A Reaction\u2013Diffusion System of General Gene Expression with Delays","display_name":"A Reaction\u2013Diffusion System of General Gene Expression with Delays","publication_year":2026,"publication_date":"2026-02-04","ids":{"openalex":"https://openalex.org/W7127621100","doi":"https://doi.org/10.3390/math14030563"},"language":"en","primary_location":{"id":"doi:10.3390/math14030563","doi":"https://doi.org/10.3390/math14030563","is_oa":true,"landing_page_url":"https://doi.org/10.3390/math14030563","pdf_url":"https://www.mdpi.com/2227-7390/14/3/563/pdf?version=1770213239","source":{"id":"https://openalex.org/S4210192031","display_name":"Mathematics","issn_l":"2227-7390","issn":["2227-7390"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2227-7390/14/3/563/pdf?version=1770213239","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5103281606","display_name":"Xiaoqin P. P. Wu","orcid":"https://orcid.org/0000-0001-9186-1903","observed_orcids":["https://orcid.org/0000-0001-9186-1903"]},"institutions":[{"id":"https://openalex.org/I61652871","display_name":"Mississippi Valley State University","ror":"https://ror.org/00rz5xc38","country_code":"US","type":"education","lineage":["https://openalex.org/I4210141039","https://openalex.org/I61652871"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Xiaoqin Wu","raw_affiliation_strings":["Department of Mathematics, Computer & Information Sciences , Mississippi Valley State University , Itta Bena , MS 38941 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Computer & Information Sciences , Mississippi Valley State University , Itta Bena , MS 38941 , USA","institution_ids":["https://openalex.org/I61652871"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5020886237","display_name":"Liancheng Wang","orcid":"https://orcid.org/0000-0002-6567-6138","observed_orcids":["https://orcid.org/0000-0002-6567-6138"]},"institutions":[{"id":"https://openalex.org/I172980758","display_name":"Kennesaw State University","ror":"https://ror.org/00jeqjx33","country_code":"US","type":"education","lineage":["https://openalex.org/I172980758"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Liancheng Wang","raw_affiliation_strings":["Department of Mathematics , Kennesaw State University , Marietta , GA 30060 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Kennesaw State University , Marietta , GA 30060 , USA","institution_ids":["https://openalex.org/I172980758"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5020886237"],"corresponding_institution_ids":["https://openalex.org/I172980758"],"apc_list":{"value":2600,"currency":"CHF","value_usd":3137},"apc_paid":{"value":2600,"currency":"CHF","value_usd":3137},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0674423,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"3","first_page":"563","last_page":"563"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.5713000297546387,"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"}},"topics":[{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.5713000297546387,"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/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.0917000025510788,"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"}},{"id":"https://openalex.org/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.09160000085830688,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/reaction-diffusion-systems","display_name":"reaction-diffusion systems","score":0.953000009059906},{"id":"https://openalex.org/keywords/gene-expression","display_name":"gene expression","score":0.9419999718666077},{"id":"https://openalex.org/keywords/time-delay","display_name":"time delay","score":0.9470000267028809},{"id":"https://openalex.org/keywords/hopf-bifurcation","display_name":"Hopf bifurcation","score":0.9290000200271606},{"id":"https://openalex.org/keywords/global-existence","display_name":"global existence","score":0.7490000128746033},{"id":"https://openalex.org/keywords/attractors","display_name":"attractors","score":0.7289999723434448},{"id":"https://openalex.org/keywords/neumann-boundary-conditions","display_name":"Neumann boundary conditions","score":0.9300000071525574},{"id":"https://openalex.org/keywords/delay-differential-equations","display_name":"delay differential equations","score":0.5070000290870667},{"id":"https://openalex.org/keywords/maximum-principle","display_name":"maximum principle","score":0.597000002861023},{"id":"https://openalex.org/keywords/steady-state-solutions","display_name":"stationary solutions","score":0.8159999847412109},{"id":"https://openalex.org/keywords/stability-of-equilibrium","display_name":"equilibrium stability","score":0.5630000233650208}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6687999963760376},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.618399977684021},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.5929999947547913},{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.541700005531311},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.525600016117096},{"id":"https://openalex.org/C90559484","wikidata":"https://www.wikidata.org/wiki/Q778379","display_name":"Expression (computer science)","level":2,"score":0.5235999822616577},{"id":"https://openalex.org/C94766913","wikidata":"https://www.wikidata.org/wiki/Q1530271","display_name":"Equilibrium point","level":3,"score":0.5101000070571899},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4982999861240387},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4884999990463257},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4740000069141388},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.44780001044273376},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4291999936103821},{"id":"https://openalex.org/C101225446","wikidata":"https://www.wikidata.org/wiki/Q740190","display_name":"Saddle-node bifurcation","level":4,"score":0.38359999656677246},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.3774000108242035},{"id":"https://openalex.org/C163681178","wikidata":"https://www.wikidata.org/wiki/Q1149279","display_name":"Neumann boundary condition","level":3,"score":0.37439998984336853},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.37139999866485596},{"id":"https://openalex.org/C155092403","wikidata":"https://www.wikidata.org/wiki/Q1785924","display_name":"Pitchfork bifurcation","level":5,"score":0.3619000017642975},{"id":"https://openalex.org/C86243350","wikidata":"https://www.wikidata.org/wiki/Q2595915","display_name":"Bifurcation diagram","level":4,"score":0.3612000048160553},{"id":"https://openalex.org/C85075877","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Bifurcation theory","level":4,"score":0.3361000120639801},{"id":"https://openalex.org/C174914120","wikidata":"https://www.wikidata.org/wiki/Q4914973","display_name":"Biological applications of bifurcation theory","level":5,"score":0.33230000734329224},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.31779998540878296},{"id":"https://openalex.org/C22257346","wikidata":"https://www.wikidata.org/wiki/Q4937510","display_name":"Bogdanov\u2013Takens bifurcation","level":5,"score":0.3059000074863434},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.301800012588501},{"id":"https://openalex.org/C192872217","wikidata":"https://www.wikidata.org/wiki/Q720574","display_name":"R\u00f6ssler attractor","level":3,"score":0.301800012588501},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.29739999771118164},{"id":"https://openalex.org/C500300565","wikidata":"https://www.wikidata.org/wiki/Q925667","display_name":"Computer simulation","level":2,"score":0.2883000075817108},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.27649998664855957},{"id":"https://openalex.org/C55610538","wikidata":"https://www.wikidata.org/wiki/Q1502581","display_name":"Transcritical bifurcation","level":5,"score":0.2702000141143799},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.26739999651908875},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.26570001244544983}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/math14030563","doi":"https://doi.org/10.3390/math14030563","is_oa":true,"landing_page_url":"https://doi.org/10.3390/math14030563","pdf_url":"https://www.mdpi.com/2227-7390/14/3/563/pdf?version=1770213239","source":{"id":"https://openalex.org/S4210192031","display_name":"Mathematics","issn_l":"2227-7390","issn":["2227-7390"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics","raw_type":"journal-article"},{"id":"doi:10.20944/preprints202512.1863.v1","doi":"https://doi.org/10.20944/preprints202512.1863.v1","is_oa":true,"landing_page_url":"https://doi.org/10.20944/preprints202512.1863.v1","pdf_url":"https://www.preprints.org/frontend/manuscript/6c1b48e7bd108c7c818356e2a6707377/download_pub","source":{"id":"https://openalex.org/S6309402219","display_name":"Preprints.org","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"posted-content"},{"id":"pmh:oai:doaj.org/article:ecb091d73df64837b1f13e1c7347e6ed","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/ecb091d73df64837b1f13e1c7347e6ed","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematics, Vol 14, Iss 3, p 563 (2026)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/math14030563","doi":"https://doi.org/10.3390/math14030563","is_oa":true,"landing_page_url":"https://doi.org/10.3390/math14030563","pdf_url":"https://www.mdpi.com/2227-7390/14/3/563/pdf?version=1770213239","source":{"id":"https://openalex.org/S4210192031","display_name":"Mathematics","issn_l":"2227-7390","issn":["2227-7390"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7127621100.pdf","grobid_xml":"https://content.openalex.org/works/W7127621100.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W335283402","https://openalex.org/W588153840","https://openalex.org/W1527296550","https://openalex.org/W1594759473","https://openalex.org/W1605753492","https://openalex.org/W1822833310","https://openalex.org/W1984507032","https://openalex.org/W1994094413","https://openalex.org/W2000040985","https://openalex.org/W2088925327","https://openalex.org/W2089560992","https://openalex.org/W2094559589","https://openalex.org/W2108123681","https://openalex.org/W2153575924","https://openalex.org/W3040500874","https://openalex.org/W4250716583","https://openalex.org/W4290420396"],"related_works":[],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"a":[3,10,30,58],"complete":[4],"analysis":[5],"is":[6,86],"presented":[7],"to":[8,66,88,100],"study":[9],"reaction\u2013diffusion":[11],"system":[12,99],"of":[13,29,37,71,78,92],"general":[14],"gene":[15],"expression":[16],"with":[17,22],"two":[18],"time":[19],"delays":[20,43],"and":[21,34,75],"Neumann":[23],"boundary":[24],"conditions.":[25],"The":[26,95],"global":[27],"existence":[28,36],"unique":[31,59],"strong":[32],"solution":[33],"the":[35,53,69,72,76,83,90,98],"an":[38],"attractor":[39],"are":[40,64,104],"established.":[41],"Using":[42],"as":[44],"bifurcation":[45,55],"parameters,":[46],"we":[47],"obtain":[48,89],"critical":[49],"values":[50],"so":[51],"that":[52],"Hopf":[54],"occurs":[56],"at":[57],"equilibrium":[60,73],"point.":[61],"Numerical":[62],"simulations":[63],"provided":[65],"illustrate":[67],"both":[68],"stability":[70],"point":[74],"emergence":[77],"bifurcations.":[79],"For":[80],"steady-state":[81],"solutions,":[82],"Maximum":[84],"Principle":[85],"used":[87],"bounds":[91],"positive":[93],"solutions.":[94],"conditions":[96],"for":[97],"have":[101],"constant":[102],"solutions":[103],"also":[105],"investigated.":[106]},"counts_by_year":[],"updated_date":"2026-10-14T16:39:01.820549","created_date":"2026-02-06T00:00:00"}