{"id":"https://openalex.org/W2805471816","doi":"https://doi.org/10.1016/j.cam.2018.04.018","title":"Mean square stability of two classes of theta methods for numerical computation and simulation of delayed stochastic Hopfield neural networks","display_name":"Mean square stability of two classes of theta methods for numerical computation and simulation of delayed stochastic Hopfield neural networks","publication_year":2018,"publication_date":"2018-05-03","ids":{"openalex":"https://openalex.org/W2805471816","doi":"https://doi.org/10.1016/j.cam.2018.04.018","mag":"2805471816"},"language":"en","primary_location":{"id":"doi:10.1016/j.cam.2018.04.018","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.cam.2018.04.018","pdf_url":null,"source":{"id":"https://openalex.org/S165473669","display_name":"Journal of Computational and Applied Mathematics","issn_l":"0377-0427","issn":["0377-0427","1879-1778"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Computational and Applied Mathematics","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/A5023940842","display_name":"Linna Liu","orcid":"https://orcid.org/0000-0001-5458-5508"},"institutions":[{"id":"https://openalex.org/I90610280","display_name":"South China University of Technology","ror":"https://ror.org/0530pts50","country_code":"CN","type":"education","lineage":["https://openalex.org/I90610280"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Linna Liu","raw_affiliation_strings":["Systems Engineering Institute, South China University of Technology, Guangzhou 510640, China"],"affiliations":[{"raw_affiliation_string":"Systems Engineering Institute, South China University of Technology, Guangzhou 510640, China","institution_ids":["https://openalex.org/I90610280"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063134490","display_name":"Feiqi Deng","orcid":"https://orcid.org/0000-0002-0257-5647"},"institutions":[{"id":"https://openalex.org/I90610280","display_name":"South China University of Technology","ror":"https://ror.org/0530pts50","country_code":"CN","type":"education","lineage":["https://openalex.org/I90610280"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Feiqi Deng","raw_affiliation_strings":["Systems Engineering Institute, South China University of Technology, Guangzhou 510640, China"],"affiliations":[{"raw_affiliation_string":"Systems Engineering Institute, South China University of Technology, Guangzhou 510640, China","institution_ids":["https://openalex.org/I90610280"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100600035","display_name":"Quanxin Zhu","orcid":"https://orcid.org/0000-0003-3130-4923"},"institutions":[{"id":"https://openalex.org/I152031979","display_name":"Nanjing Normal University","ror":"https://ror.org/036trcv74","country_code":"CN","type":"education","lineage":["https://openalex.org/I152031979"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Quanxin Zhu","raw_affiliation_strings":["School of Mathematical Sciences and Institute of Finance and Statistics, Nanjing Normal University, Nanjing, 210023, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences and Institute of Finance and Statistics, Nanjing Normal University, Nanjing, 210023, China","institution_ids":["https://openalex.org/I152031979"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5063134490"],"corresponding_institution_ids":["https://openalex.org/I90610280"],"apc_list":{"value":3040,"currency":"USD","value_usd":3040},"apc_paid":null,"fwci":0.9749,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.78531715,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"343","issue":null,"first_page":"428","last_page":"447"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":1.0,"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/T10320","display_name":"Neural Networks and Applications","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9962000250816345,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8173335790634155},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.6681775450706482},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5983749628067017},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.526877224445343},{"id":"https://openalex.org/keywords/mean-square","display_name":"Mean square","score":0.500340461730957},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.49493545293807983},{"id":"https://openalex.org/keywords/numerical-stability","display_name":"Numerical stability","score":0.49481576681137085},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.46859994530677795},{"id":"https://openalex.org/keywords/square","display_name":"Square (algebra)","score":0.4299963414669037},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.4297105073928833},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2791668772697449},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.1423760950565338},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13861417770385742},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06790465116500854}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8173335790634155},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.6681775450706482},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5983749628067017},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.526877224445343},{"id":"https://openalex.org/C2988709989","wikidata":"https://www.wikidata.org/wiki/Q85784623","display_name":"Mean square","level":2,"score":0.500340461730957},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.49493545293807983},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.49481576681137085},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.46859994530677795},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.4299963414669037},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4297105073928833},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2791668772697449},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.1423760950565338},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13861417770385742},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06790465116500854},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/j.cam.2018.04.018","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.cam.2018.04.018","pdf_url":null,"source":{"id":"https://openalex.org/S165473669","display_name":"Journal of Computational and Applied Mathematics","issn_l":"0377-0427","issn":["0377-0427","1879-1778"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Computational and Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2599632846","display_name":null,"funder_award_id":"61503142","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2817589173","display_name":null,"funder_award_id":"61573156","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7983794113","display_name":null,"funder_award_id":"61733008","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W600357457","https://openalex.org/W1275718198","https://openalex.org/W1583371091","https://openalex.org/W1962309857","https://openalex.org/W1964221133","https://openalex.org/W1975417422","https://openalex.org/W1983176089","https://openalex.org/W1993539434","https://openalex.org/W1993560184","https://openalex.org/W2004777103","https://openalex.org/W2012747579","https://openalex.org/W2033096483","https://openalex.org/W2035646573","https://openalex.org/W2039261336","https://openalex.org/W2039617089","https://openalex.org/W2042190725","https://openalex.org/W2042649727","https://openalex.org/W2043241145","https://openalex.org/W2051212416","https://openalex.org/W2062224371","https://openalex.org/W2062564145","https://openalex.org/W2070536907","https://openalex.org/W2071642449","https://openalex.org/W2074297437","https://openalex.org/W2081875352","https://openalex.org/W2082169498","https://openalex.org/W2082572397","https://openalex.org/W2087446935","https://openalex.org/W2104659821","https://openalex.org/W2118068698","https://openalex.org/W2162800561","https://openalex.org/W2162847266","https://openalex.org/W6618047829","https://openalex.org/W6648788299","https://openalex.org/W6660465940"],"related_works":["https://openalex.org/W1786566370","https://openalex.org/W2102789413","https://openalex.org/W2370499858","https://openalex.org/W2096467061","https://openalex.org/W1532287630","https://openalex.org/W2745594548","https://openalex.org/W2902606351","https://openalex.org/W2940603871","https://openalex.org/W2082296130","https://openalex.org/W4299508867"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3}],"updated_date":"2026-03-10T14:07:55.174380","created_date":"2025-10-10T00:00:00"}
