{"id":"https://openalex.org/W2076611992","doi":"https://doi.org/10.1142/s0218127409023482","title":"HOPF BIFURCATION ANALYSIS OF DIFFUSIVE BASS MODEL WITH DELAY UNDER \"NEGATIVE-WORD-OF-MOUTH\"","display_name":"HOPF BIFURCATION ANALYSIS OF DIFFUSIVE BASS MODEL WITH DELAY UNDER \"NEGATIVE-WORD-OF-MOUTH\"","publication_year":2009,"publication_date":"2009-03-01","ids":{"openalex":"https://openalex.org/W2076611992","doi":"https://doi.org/10.1142/s0218127409023482","mag":"2076611992"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127409023482","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127409023482","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/A5089468278","display_name":"A.W. Wijeratne","orcid":"https://orcid.org/0000-0002-0513-1582"},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]},{"id":"https://openalex.org/I908128300","display_name":"Sabaragamuwa University of Sri Lanka","ror":"https://ror.org/045vwzt11","country_code":"LK","type":"education","lineage":["https://openalex.org/I908128300"]}],"countries":["CN","LK"],"is_corresponding":false,"raw_author_name":"A. W. WIJERATNE","raw_affiliation_strings":["Department of Agri-Business Management, Sabaragamuwa University of Sri Lanka, Belihuloya 70140, Sri Lanka","Department of Mathematics, Harbin Institute of Technology, Harbin 150001, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Agri-Business Management, Sabaragamuwa University of Sri Lanka, Belihuloya 70140, Sri Lanka","institution_ids":["https://openalex.org/I908128300"]},{"raw_affiliation_string":"Department of Mathematics, Harbin Institute of Technology, Harbin 150001, P. R. China","institution_ids":["https://openalex.org/I204983213"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103703430","display_name":"Ying Su","orcid":null},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"YING SU","raw_affiliation_strings":["Department of Mathematics, Harbin Institute of Technology, Harbin 150001, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Harbin Institute of Technology, Harbin 150001, P. R. China","institution_ids":["https://openalex.org/I204983213"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5051954401","display_name":"Junjie Wei","orcid":"https://orcid.org/0000-0001-5753-2946"},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"JUNJIE WEI","raw_affiliation_strings":["Department of Mathematics, Harbin Institute of Technology, Harbin 150001, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Harbin Institute of Technology, Harbin 150001, P. R. China","institution_ids":["https://openalex.org/I204983213"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.2298,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.81987256,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"19","issue":"03","first_page":"1059","last_page":"1067"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12659","display_name":"Innovation Diffusion and Forecasting","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T12659","display_name":"Innovation Diffusion and Forecasting","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.9868000149726868,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11437","display_name":"Digital Platforms and Economics","score":0.9652000069618225,"subfield":{"id":"https://openalex.org/subfields/1408","display_name":"Strategy and Management"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/hopf-bifurcation","display_name":"Hopf bifurcation","score":0.7478893399238586},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6196038722991943},{"id":"https://openalex.org/keywords/bass","display_name":"Bass (fish)","score":0.5999297499656677},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.48361340165138245},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.44344648718833923},{"id":"https://openalex.org/keywords/instability","display_name":"Instability","score":0.43399906158447266},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.362604558467865},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3534417152404785},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.23590490221977234},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.12751591205596924},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.10499930381774902},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.07518178224563599}],"concepts":[{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.7478893399238586},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6196038722991943},{"id":"https://openalex.org/C2777182073","wikidata":"https://www.wikidata.org/wiki/Q1224135","display_name":"Bass (fish)","level":2,"score":0.5999297499656677},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.48361340165138245},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.44344648718833923},{"id":"https://openalex.org/C207821765","wikidata":"https://www.wikidata.org/wiki/Q405372","display_name":"Instability","level":2,"score":0.43399906158447266},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.362604558467865},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3534417152404785},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.23590490221977234},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.12751591205596924},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.10499930381774902},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.07518178224563599},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127409023482","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127409023482","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":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1822833310","https://openalex.org/W1967649473","https://openalex.org/W1990406041","https://openalex.org/W2009433941","https://openalex.org/W2031634382","https://openalex.org/W2033270072","https://openalex.org/W2040364271","https://openalex.org/W2042372440","https://openalex.org/W2044298660","https://openalex.org/W2056316302","https://openalex.org/W2061781713","https://openalex.org/W2073148390","https://openalex.org/W2095851786","https://openalex.org/W2126974268","https://openalex.org/W2153543940","https://openalex.org/W2156069601","https://openalex.org/W3123954725","https://openalex.org/W4253543067","https://openalex.org/W4254175127","https://openalex.org/W4255777804"],"related_works":["https://openalex.org/W587891163","https://openalex.org/W1991830762","https://openalex.org/W2782013024","https://openalex.org/W2011560150","https://openalex.org/W2076114088","https://openalex.org/W2494322668","https://openalex.org/W2134105472","https://openalex.org/W611295337","https://openalex.org/W4385805634","https://openalex.org/W2006928199"],"abstract_inverted_index":{"The":[0,20,36,60,72],"original":[1],"Bass":[2],"product":[3,122],"growth":[4,49],"model":[5],"has":[6],"been":[7],"modified":[8],"in":[9,123],"this":[10],"paper":[11],"by":[12,119],"incorporating":[13],"a":[14,18,57,92,104],"diffusion":[15,79],"term":[16],"and":[17],"delay.":[19],"imitation":[21],"parameter":[22],"\u03b2":[23,54],"is":[24,103],"assumed":[25],"to":[26,68],"be":[27,117],"negative":[28],"which":[29],"represents":[30],"the":[31,42,46,63,69,110,121],"effect":[32],"of":[33,38,45,62,65,95,114],"\"negative-word-of-mouth\"":[34],"(NWOM).":[35],"occurrence":[37],"Hopf":[39],"bifurcation":[40],"at":[41,77],"positive":[43,74],"equilibrium":[44,75],"remaining":[47],"market":[48],"u*":[50,115],"was":[51],"proved":[52],"as":[53],"passes":[55],"through":[56],"critical":[58,105],"value.":[59],"analysis":[61],"distribution":[64],"eigenvalues":[66],"led":[67],"following":[70],"conclusion.":[71],"unstable":[73],"state":[76,113],"zero":[78],"(d":[80],"=":[81],"0)":[82],"under":[83],"NWOM":[84],"becomes":[85],"stable":[86,112],"when":[87,101],"d":[88],"&gt;":[89],"0":[90],"for":[91,109],"wide":[93],"range":[94],"\u03b2.":[96],"This":[97],"observation":[98],"suggests":[99],"that":[100],"there":[102],"NWOM,":[106],"favorable":[107],"conditions":[108],"future":[111],"could":[116],"achieved":[118],"promoting":[120],"space":[124],"(new":[125],"geographical":[126],"areas).":[127]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
