{"id":"https://openalex.org/W2086224821","doi":"https://doi.org/10.1155/2013/625028","title":"Forecasting New Product Diffusion Using Grey Time-Delayed Verhulst Model","display_name":"Forecasting New Product Diffusion Using Grey Time-Delayed Verhulst Model","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2086224821","doi":"https://doi.org/10.1155/2013/625028","mag":"2086224821"},"language":"en","primary_location":{"id":"doi:10.1155/2013/625028","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/625028","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/625028.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/jam/2013/625028.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5108047883","display_name":"Yuhong Wang","orcid":"https://orcid.org/0000-0002-8549-7495"},"institutions":[{"id":"https://openalex.org/I111599522","display_name":"Jiangnan University","ror":"https://ror.org/04mkzax54","country_code":"CN","type":"education","lineage":["https://openalex.org/I111599522"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yuhong Wang","raw_affiliation_strings":["School of Business, Jiangnan University, Wuxi 214122, China"],"raw_orcid":"https://orcid.org/0000-0002-8549-7495","affiliations":[{"raw_affiliation_string":"School of Business, Jiangnan University, Wuxi 214122, China","institution_ids":["https://openalex.org/I111599522"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101439014","display_name":"Yang Shu-lin","orcid":"https://orcid.org/0000-0001-9650-3347"},"institutions":[{"id":"https://openalex.org/I111599522","display_name":"Jiangnan University","ror":"https://ror.org/04mkzax54","country_code":"CN","type":"education","lineage":["https://openalex.org/I111599522"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shulin Yang","raw_affiliation_strings":["School of Business, Jiangnan University, Wuxi 214122, China"],"raw_orcid":"https://orcid.org/0000-0001-9650-3347","affiliations":[{"raw_affiliation_string":"School of Business, Jiangnan University, Wuxi 214122, China","institution_ids":["https://openalex.org/I111599522"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103141060","display_name":"Wuyong Qian","orcid":"https://orcid.org/0000-0002-7974-3450"},"institutions":[{"id":"https://openalex.org/I111599522","display_name":"Jiangnan University","ror":"https://ror.org/04mkzax54","country_code":"CN","type":"education","lineage":["https://openalex.org/I111599522"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wuyong Qian","raw_affiliation_strings":["School of Business, Jiangnan University, Wuxi 214122, China"],"raw_orcid":"https://orcid.org/0000-0002-7974-3450","affiliations":[{"raw_affiliation_string":"School of Business, Jiangnan University, Wuxi 214122, China","institution_ids":["https://openalex.org/I111599522"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5076886940","display_name":"Xiaozhong Li","orcid":"https://orcid.org/0000-0002-2911-7814"},"institutions":[{"id":"https://openalex.org/I111599522","display_name":"Jiangnan University","ror":"https://ror.org/04mkzax54","country_code":"CN","type":"education","lineage":["https://openalex.org/I111599522"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaozhong Li","raw_affiliation_strings":["School of Business, Jiangnan University, Wuxi 214122, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Business, Jiangnan University, Wuxi 214122, China","institution_ids":["https://openalex.org/I111599522"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5108047883"],"corresponding_institution_ids":["https://openalex.org/I111599522"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.8524,"has_fulltext":true,"cited_by_count":13,"citation_normalized_percentile":{"value":0.78824333,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"2013","issue":null,"first_page":"1","last_page":"6"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12368","display_name":"Grey System Theory Applications","score":0.9997000098228455,"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/T12368","display_name":"Grey System Theory Applications","score":0.9997000098228455,"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/T14369","display_name":"Diverse Interdisciplinary Research Innovations","score":0.9341999888420105,"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/T12659","display_name":"Innovation Diffusion and Forecasting","score":0.9200000166893005,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.5320514440536499},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5313135981559753},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.5208792686462402},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.4728788733482361},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4125932455062866},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.3960501551628113},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.38577592372894287},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.29324871301651},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06951829791069031},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.04136011004447937},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.04004925489425659}],"concepts":[{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.5320514440536499},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5313135981559753},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.5208792686462402},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.4728788733482361},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4125932455062866},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.3960501551628113},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38577592372894287},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.29324871301651},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06951829791069031},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.04136011004447937},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.04004925489425659},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2013/625028","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/625028","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/625028.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jam/1394808307","is_oa":false,"landing_page_url":"https://projecteuclid.org/euclid.jam/1394808307","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:RePEc:hin:jnljam:625028","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/JAM/2013/625028.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:614ab7d67aa44e67a278afefd36f360a","is_oa":true,"landing_page_url":"https://doaj.org/article/614ab7d67aa44e67a278afefd36f360a","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,"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":"Journal of Applied Mathematics, Vol 2013 (2013)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2013/625028","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/625028","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/625028.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1605580224","display_name":null,"funder_award_id":"12AZD111","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2551152689","display_name":null,"funder_award_id":"2010WQN004","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3325983871","display_name":null,"funder_award_id":"12DDA011","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4541934415","display_name":null,"funder_award_id":"2010WQN004","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4700221461","display_name":null,"funder_award_id":"2011SJD630009","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5633541862","display_name":null,"funder_award_id":"71301061","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5743142721","display_name":null,"funder_award_id":"2011SJD630009","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5916591386","display_name":null,"funder_award_id":"12YJCZH207","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6087398144","display_name":null,"funder_award_id":"12AZD111","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6345040315","display_name":null,"funder_award_id":"EFA110351","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7298795993","display_name":null,"funder_award_id":"12DDA011","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7605607547","display_name":null,"funder_award_id":"EFA110351","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8431077363","display_name":null,"funder_award_id":"71301061","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G989492557","display_name":null,"funder_award_id":"12YJCZH207","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321106","display_name":"Ministry of Education of the People's Republic of China","ror":"https://ror.org/01mv9t934"},{"id":"https://openalex.org/F4320321605","display_name":"Government of Jiangsu Province","ror":"https://ror.org/004svx814"},{"id":"https://openalex.org/F4320322296","display_name":"Jiangnan University","ror":"https://ror.org/04mkzax54"},{"id":"https://openalex.org/F4320335221","display_name":"College of Humanities and Social Sciences, United Arab Emirates University","ror":"https://ror.org/01km6p862"},{"id":"https://openalex.org/F4320335869","display_name":"National Social Science Fund of China","ror":null},{"id":"https://openalex.org/F4320336751","display_name":"Science Foundation of Ministry of Education of China","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2086224821.pdf","grobid_xml":"https://content.openalex.org/works/W2086224821.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W1964585049","https://openalex.org/W1965425305","https://openalex.org/W1997439963","https://openalex.org/W2003037801","https://openalex.org/W2004199150","https://openalex.org/W2007666989","https://openalex.org/W2044448513","https://openalex.org/W2083038452","https://openalex.org/W2117603680","https://openalex.org/W2352276815","https://openalex.org/W2365032046","https://openalex.org/W2371835455","https://openalex.org/W2785283270"],"related_works":["https://openalex.org/W1922851888","https://openalex.org/W2406961220","https://openalex.org/W2046260256","https://openalex.org/W4232468313","https://openalex.org/W2386796262","https://openalex.org/W4242249046","https://openalex.org/W3162882601","https://openalex.org/W3214485701","https://openalex.org/W3177740930","https://openalex.org/W3102283898"],"abstract_inverted_index":{"Taking":[0],"account":[1],"of":[2,8,28,36,45,63,78],"the":[3,13,26,43,54,71,83,91],"time-delayed":[4,14,22,65,72,93],"phenomenon":[5],"in":[6,97],"diffusion":[7,80],"new":[9],"products,":[10],"we":[11],"propose":[12],"Verhulst":[15,23,57,66,94],"model":[16,24,39,58,67,95],"and":[17],"then":[18],"establish":[19],"a":[20,60],"grey":[21,29,56,64,92],"using":[25,90],"method":[27],"differential":[30],"equations.":[31],"The":[32,50],"related":[33],"parameter":[34],"packets":[35],"this":[37,98],"novel":[38],"are":[40],"obtained":[41],"under":[42],"rule":[44],"ordinary":[46],"least":[47],"squares":[48],"(OLS).":[49],"results":[51],"show":[52],"that":[53,82],"traditional":[55],"is":[59,86],"special":[61],"example":[62,77],"which":[68],"can":[69],"reflect":[70],"information":[73],"effectively.":[74],"A":[75],"practical":[76],"market":[79],"shows":[81],"modeling":[84],"accuracy":[85],"remarkably":[87],"improved":[88],"by":[89],"presented":[96],"paper.":[99]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}