{"id":"https://openalex.org/W4283735891","doi":"https://doi.org/10.1142/s0218127422501097","title":"Bifurcation Analysis of a Reaction\u2013Diffusion Rumor Spreading Model with Nonsmooth Control","display_name":"Bifurcation Analysis of a Reaction\u2013Diffusion Rumor Spreading Model with Nonsmooth Control","publication_year":2022,"publication_date":"2022-06-30","ids":{"openalex":"https://openalex.org/W4283735891","doi":"https://doi.org/10.1142/s0218127422501097"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127422501097","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127422501097","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/A5057711793","display_name":"Linhe Zhu","orcid":"https://orcid.org/0000-0002-2457-4821"},"institutions":[{"id":"https://openalex.org/I115592961","display_name":"Jiangsu University","ror":"https://ror.org/03jc41j30","country_code":"CN","type":"education","lineage":["https://openalex.org/I115592961"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Linhe Zhu","raw_affiliation_strings":["School of Mathematical Sciences, Jiangsu University, Zhenjiang 212013, P. R. China"],"raw_orcid":"https://orcid.org/0000-0002-2457-4821","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Jiangsu University, Zhenjiang 212013, P. R. China","institution_ids":["https://openalex.org/I115592961"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037819741","display_name":"Wenxin Zheng","orcid":null},"institutions":[{"id":"https://openalex.org/I115592961","display_name":"Jiangsu University","ror":"https://ror.org/03jc41j30","country_code":"CN","type":"education","lineage":["https://openalex.org/I115592961"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wenxin Zheng","raw_affiliation_strings":["School of Mathematical Sciences, Jiangsu University, Zhenjiang 212013, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Jiangsu University, Zhenjiang 212013, P. R. China","institution_ids":["https://openalex.org/I115592961"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100745894","display_name":"Xuebing Zhang","orcid":"https://orcid.org/0000-0003-0561-5576"},"institutions":[{"id":"https://openalex.org/I200845125","display_name":"Nanjing University of Information Science and Technology","ror":"https://ror.org/02y0rxk19","country_code":"CN","type":"education","lineage":["https://openalex.org/I200845125"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xuebing Zhang","raw_affiliation_strings":["College of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, P. R. China","institution_ids":["https://openalex.org/I200845125"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5057711793"],"corresponding_institution_ids":["https://openalex.org/I115592961"],"apc_list":null,"apc_paid":null,"fwci":1.1256,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.77103093,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":98},"biblio":{"volume":"32","issue":"08","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12592","display_name":"Opinion Dynamics and Social Influence","score":0.9986000061035156,"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/T12592","display_name":"Opinion Dynamics and Social Influence","score":0.9986000061035156,"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/T10064","display_name":"Complex Network Analysis Techniques","score":0.9940999746322632,"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":0.9925000071525574,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/rumor","display_name":"Rumor","score":0.9386343955993652},{"id":"https://openalex.org/keywords/hopf-bifurcation","display_name":"Hopf bifurcation","score":0.6110279560089111},{"id":"https://openalex.org/keywords/discontinuity","display_name":"Discontinuity (linguistics)","score":0.5854562520980835},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.5470404028892517},{"id":"https://openalex.org/keywords/equilibrium-point","display_name":"Equilibrium point","score":0.5374292731285095},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5163211226463318},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4880041182041168},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.45496827363967896},{"id":"https://openalex.org/keywords/reaction\u2013diffusion-system","display_name":"Reaction\u2013diffusion system","score":0.44544142484664917},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.43686485290527344},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.42663419246673584},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.4151241183280945},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.36614078283309937},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.3529255986213684},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.30624598264694214},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.23360306024551392},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.19963416457176208},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08304950594902039}],"concepts":[{"id":"https://openalex.org/C2780469804","wikidata":"https://www.wikidata.org/wiki/Q878352","display_name":"Rumor","level":2,"score":0.9386343955993652},{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.6110279560089111},{"id":"https://openalex.org/C2777042112","wikidata":"https://www.wikidata.org/wiki/Q5281658","display_name":"Discontinuity (linguistics)","level":2,"score":0.5854562520980835},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.5470404028892517},{"id":"https://openalex.org/C94766913","wikidata":"https://www.wikidata.org/wiki/Q1530271","display_name":"Equilibrium point","level":3,"score":0.5374292731285095},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5163211226463318},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4880041182041168},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.45496827363967896},{"id":"https://openalex.org/C121231716","wikidata":"https://www.wikidata.org/wiki/Q901210","display_name":"Reaction\u2013diffusion system","level":2,"score":0.44544142484664917},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.43686485290527344},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42663419246673584},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4151241183280945},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.36614078283309937},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.3529255986213684},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.30624598264694214},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.23360306024551392},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.19963416457176208},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08304950594902039},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C39549134","wikidata":"https://www.wikidata.org/wiki/Q133080","display_name":"Public relations","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/s0218127422501097","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127422501097","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":[{"display_name":"Decent work and economic growth","score":0.5799999833106995,"id":"https://metadata.un.org/sdg/8"}],"awards":[{"id":"https://openalex.org/G1804070562","display_name":null,"funder_award_id":"2019M661732","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G2472306845","display_name":null,"funder_award_id":"BK20190836","funder_id":"https://openalex.org/F4320322769","funder_display_name":"Natural Science Foundation of Jiangsu Province"},{"id":"https://openalex.org/G4540700603","display_name":null,"funder_award_id":"12002135","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5737974334","display_name":null,"funder_award_id":"19KJB110001","funder_id":"https://openalex.org/F4320335440","funder_display_name":"Natural Science Research of Jiangsu Higher Education Institutions of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321543","display_name":"China Postdoctoral Science Foundation","ror":"https://ror.org/0426zh255"},{"id":"https://openalex.org/F4320322769","display_name":"Natural Science Foundation of Jiangsu Province","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335440","display_name":"Natural Science Research of Jiangsu Higher Education Institutions of China","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W29843464","https://openalex.org/W1478686509","https://openalex.org/W2021600996","https://openalex.org/W2050316258","https://openalex.org/W2089394618","https://openalex.org/W2091947980","https://openalex.org/W2111574777","https://openalex.org/W2463473857","https://openalex.org/W2615399417","https://openalex.org/W2770246234","https://openalex.org/W2790379188","https://openalex.org/W2914804271","https://openalex.org/W2921086346","https://openalex.org/W2921396506","https://openalex.org/W2940275301","https://openalex.org/W2944790101","https://openalex.org/W2949760806","https://openalex.org/W2951907455","https://openalex.org/W2961041337","https://openalex.org/W2962077946","https://openalex.org/W2998097374","https://openalex.org/W2999142346","https://openalex.org/W3013846983","https://openalex.org/W3033625896","https://openalex.org/W3035605930","https://openalex.org/W3046677889","https://openalex.org/W3080711769","https://openalex.org/W3089764765","https://openalex.org/W4232523802","https://openalex.org/W4312587821"],"related_works":["https://openalex.org/W3150441072","https://openalex.org/W2001031286","https://openalex.org/W3158507292","https://openalex.org/W2898039612","https://openalex.org/W4307948965","https://openalex.org/W2371933884","https://openalex.org/W2463473857","https://openalex.org/W4283735891","https://openalex.org/W2091792699","https://openalex.org/W2624346271"],"abstract_inverted_index":{"Rumors":[0],"may":[1],"cause":[2],"serious":[3],"harm":[4],"to":[5,21],"social":[6],"productivity":[7],"and":[8,53,76,88,101,118],"life.":[9],"Studying":[10],"the":[11,27,71,90,107,120,126,133,136],"dynamics":[12],"of":[13,74,92,98,109,122,135],"rumor":[14,39,51,78,110],"propagation":[15,56],"can":[16],"help":[17],"provide":[18],"corresponding":[19],"countermeasures":[20],"control":[22],"communication":[23,48],"effectively.":[24],"Based":[25],"on":[26],"classic":[28],"[Formula:":[29],"see":[30],"text]":[31],"infectious":[32],"disease":[33],"model,":[34,62],"this":[35,61],"paper":[36],"studies":[37],"a":[38,43],"spreading":[40],"model":[41],"with":[42],"time":[44],"delay":[45,49],"caused":[46],"by":[47,139],"between":[50],"communicators":[52],"nonsmooth":[54,77],"threshold":[55],"function":[57],"in":[58],"reality.":[59],"In":[60,104],"we":[63,80,112],"solve":[64],"non-negative":[65,85],"equilibrium":[66,86],"points":[67,87],"firstly.":[68],"By":[69],"analyzing":[70],"characteristic":[72],"equations":[73],"smooth":[75],"systems,":[79],"establish":[81],"local":[82],"stability":[83],"at":[84],"find":[89],"existence":[91],"Hopf":[93,123],"bifurcation":[94,124],"from":[95],"two":[96,116],"aspects":[97],"diffusion":[99],"coefficient":[100],"delay,":[102],"respectively.":[103],"addition,":[105],"considering":[106],"discontinuity":[108],"system,":[111],"separate":[113],"it":[114],"into":[115],"systems":[117],"get":[119],"condition":[121],"when":[125],"system":[127],"is":[128],"discontinuous.":[129],"We":[130],"further":[131],"verify":[132],"feasibility":[134],"theoretical":[137],"results":[138],"simulation":[140],"results.":[141]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":3}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
