{"id":"https://openalex.org/W2345529822","doi":"https://doi.org/10.1142/s0218127416500620","title":"Zeros of a Class of Transcendental Equation with Application to Bifurcation of DDE","display_name":"Zeros of a Class of Transcendental Equation with Application to Bifurcation of DDE","publication_year":2016,"publication_date":"2016-04-01","ids":{"openalex":"https://openalex.org/W2345529822","doi":"https://doi.org/10.1142/s0218127416500620","mag":"2345529822"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127416500620","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127416500620","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/A5016962594","display_name":"Kit Ian Kou","orcid":"https://orcid.org/0000-0003-1924-9087"},"institutions":[{"id":"https://openalex.org/I119045251","display_name":"Huaqiao University","ror":"https://ror.org/03frdh605","country_code":"CN","type":"education","lineage":["https://openalex.org/I119045251"]},{"id":"https://openalex.org/I204512498","display_name":"University of Macau","ror":"https://ror.org/01r4q9n85","country_code":"MO","type":"education","lineage":["https://openalex.org/I204512498"]}],"countries":["CN","MO"],"is_corresponding":true,"raw_author_name":"Kit Ian Kou","raw_affiliation_strings":["Department of Mathematics, Faculty of Science and Technology, University of Macau, Macau","School of Mathematical Sciences, Huaqiao University, 362021, Quanzhou, Fujian, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science and Technology, University of Macau, Macau","institution_ids":["https://openalex.org/I204512498"]},{"raw_affiliation_string":"School of Mathematical Sciences, Huaqiao University, 362021, Quanzhou, Fujian, P. R. China","institution_ids":["https://openalex.org/I119045251"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091595646","display_name":"Yijun Lou","orcid":"https://orcid.org/0000-0003-3864-2001"},"institutions":[{"id":"https://openalex.org/I14243506","display_name":"Hong Kong Polytechnic University","ror":"https://ror.org/0030zas98","country_code":"HK","type":"education","lineage":["https://openalex.org/I14243506"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Yijun Lou","raw_affiliation_strings":["Department of Applied Mathematics, The Hongkong Polytechnic University, Hongkong"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, The Hongkong Polytechnic University, Hongkong","institution_ids":["https://openalex.org/I14243506"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5112105801","display_name":"Yong-Hui Xia","orcid":null},"institutions":[{"id":"https://openalex.org/I119045251","display_name":"Huaqiao University","ror":"https://ror.org/03frdh605","country_code":"CN","type":"education","lineage":["https://openalex.org/I119045251"]},{"id":"https://openalex.org/I135237710","display_name":"Zhejiang Normal University","ror":"https://ror.org/01vevwk45","country_code":"CN","type":"education","lineage":["https://openalex.org/I135237710"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yong-Hui Xia","raw_affiliation_strings":["Department of Mathematics, Zhejiang Normal University, 321004, Jinhua, Zhejiang, P. R. China","School of Mathematical Sciences, Huaqiao University, 362021, Quanzhou, Fujian, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Zhejiang Normal University, 321004, Jinhua, Zhejiang, P. R. China","institution_ids":["https://openalex.org/I135237710"]},{"raw_affiliation_string":"School of Mathematical Sciences, Huaqiao University, 362021, Quanzhou, Fujian, P. R. China","institution_ids":["https://openalex.org/I119045251"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5016962594"],"corresponding_institution_ids":["https://openalex.org/I119045251","https://openalex.org/I204512498"],"apc_list":null,"apc_paid":null,"fwci":0.9254,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.81029976,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"26","issue":"04","first_page":"1650062","last_page":"1650062"},"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":0.9995999932289124,"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":0.9995999932289124,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9958999752998352,"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9901000261306763,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/transcendental-equation","display_name":"Transcendental equation","score":0.7891905307769775},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7789345383644104},{"id":"https://openalex.org/keywords/transcendental-number","display_name":"Transcendental number","score":0.7690964937210083},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.6710187196731567},{"id":"https://openalex.org/keywords/transcendental-function","display_name":"Transcendental function","score":0.564516544342041},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.545412003993988},{"id":"https://openalex.org/keywords/bifurcation-theory","display_name":"Bifurcation theory","score":0.4866860508918762},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.4634734094142914},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.43994638323783875},{"id":"https://openalex.org/keywords/characteristic-equation","display_name":"Characteristic equation","score":0.4392523765563965},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3880818486213684},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.30611956119537354},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10425949096679688},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07827585935592651},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.07738280296325684}],"concepts":[{"id":"https://openalex.org/C139609574","wikidata":"https://www.wikidata.org/wiki/Q2273509","display_name":"Transcendental equation","level":3,"score":0.7891905307769775},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7789345383644104},{"id":"https://openalex.org/C188370112","wikidata":"https://www.wikidata.org/wiki/Q173091","display_name":"Transcendental number","level":2,"score":0.7690964937210083},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.6710187196731567},{"id":"https://openalex.org/C43321923","wikidata":"https://www.wikidata.org/wiki/Q864333","display_name":"Transcendental function","level":2,"score":0.564516544342041},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.545412003993988},{"id":"https://openalex.org/C85075877","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Bifurcation theory","level":4,"score":0.4866860508918762},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.4634734094142914},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.43994638323783875},{"id":"https://openalex.org/C53744967","wikidata":"https://www.wikidata.org/wiki/Q1062971","display_name":"Characteristic equation","level":3,"score":0.4392523765563965},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3880818486213684},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.30611956119537354},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10425949096679688},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07827585935592651},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.07738280296325684},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218127416500620","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127416500620","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:ira.lib.polyu.edu.hk:10397/61472","is_oa":false,"landing_page_url":"http://hdl.handle.net/10397/61472","pdf_url":null,"source":{"id":"https://openalex.org/S4306400205","display_name":"PolyU Institutional Research Archive (Hong Kong Polytechnic University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I14243506","host_organization_name":"Hong Kong Polytechnic University","host_organization_lineage":["https://openalex.org/I14243506"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal/Magazine Article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/13","display_name":"Climate action","score":0.8199999928474426}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W1518049944","https://openalex.org/W1531715726","https://openalex.org/W1608528587","https://openalex.org/W1967845255","https://openalex.org/W1981721930","https://openalex.org/W2005946114","https://openalex.org/W2007456116","https://openalex.org/W2007872151","https://openalex.org/W2013235495","https://openalex.org/W2032169065","https://openalex.org/W2036308036","https://openalex.org/W2056170808","https://openalex.org/W2062210472","https://openalex.org/W2068386305","https://openalex.org/W2078046964","https://openalex.org/W2092208058","https://openalex.org/W2095097511","https://openalex.org/W2119729354","https://openalex.org/W2121419978","https://openalex.org/W2135502159","https://openalex.org/W2136003379","https://openalex.org/W2163947014","https://openalex.org/W2167473924","https://openalex.org/W3100265151","https://openalex.org/W4300833285"],"related_works":["https://openalex.org/W3014029144","https://openalex.org/W4300089223","https://openalex.org/W2074397670","https://openalex.org/W4387814077","https://openalex.org/W2041431871","https://openalex.org/W4378448846","https://openalex.org/W2233678604","https://openalex.org/W1556216774","https://openalex.org/W2965342179","https://openalex.org/W3122176387"],"abstract_inverted_index":{"Zeros":[0],"of":[1,4,29,31,67,69,102],"a":[2,87],"class":[3],"transcendental":[5,33,71],"equation":[6,34],"with":[7],"small":[8,110],"parameter":[9,56,111],"[Formula:":[10,39,51,60],"see":[11,40,52,61],"text]":[12,41,53],"are":[13,79],"considered":[14],"in":[15,23,86,90],"this":[16],"paper.":[17],"There":[18],"have":[19],"been":[20],"many":[21],"works":[22],"the":[24,27,32,37,58,65,76,83,91,96,100,109,125],"literature":[25],"considering":[26],"distribution":[28,66],"zeros":[30,68],"by":[35],"choosing":[36],"delay":[38,59],"as":[42,54,108],"bifurcation":[43,55,84],"parameter.":[44],"Different":[45],"from":[46],"standard":[47],"consideration,":[48],"we":[49],"choose":[50],"(not":[57],"text])":[62],"to":[63,82,123],"discuss":[64],"such":[70],"equation.":[72],"After":[73],"mathematical":[74],"analysis,":[75],"obtained":[77],"results":[78],"successfully":[80],"applied":[81],"analysis":[85],"biological":[88],"model":[89],"real":[92,97],"word":[93],"phenomenon.":[94],"In":[95],"world":[98],"model,":[99],"effect":[101],"climate":[103],"changes":[104],"can":[105,114],"be":[106],"seen":[107],"perturbation,":[112],"which":[113],"induce":[115],"bifurcations":[116],"and":[117,127],"instability.":[118],"We":[119],"present":[120],"two":[121],"methods":[122],"analyze":[124],"stability":[126],"bifurcations.":[128]},"counts_by_year":[{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2016,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}