{"id":"https://openalex.org/W2013110593","doi":"https://doi.org/10.1155/2014/787568","title":"Exponential Stability for Impulsive Stochastic Nonlinear Network Systems with Time Delay","display_name":"Exponential Stability for Impulsive Stochastic Nonlinear Network Systems with Time Delay","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2013110593","doi":"https://doi.org/10.1155/2014/787568","mag":"2013110593"},"language":"en","primary_location":{"id":"doi:10.1155/2014/787568","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2014/787568","pdf_url":"https://downloads.hindawi.com/journals/jam/2014/787568.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/2014/787568.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036712571","display_name":"Lanping Chen","orcid":"https://orcid.org/0000-0001-8122-9015"},"institutions":[{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]},{"id":"https://openalex.org/I4210153482","display_name":"Changzhou University","ror":"https://ror.org/04ymgwq66","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210153482"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Lanping Chen","raw_affiliation_strings":["College of Information and Engineering Science, Changzhou University, Jiangsu 213164, China","School of Electronic, Information and Electrical Engineering, Shanghai Jiaotong University, Shanghai 200240, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Information and Engineering Science, Changzhou University, Jiangsu 213164, China","institution_ids":["https://openalex.org/I4210153482"]},{"raw_affiliation_string":"School of Electronic, Information and Electrical Engineering, Shanghai Jiaotong University, Shanghai 200240, China","institution_ids":["https://openalex.org/I183067930"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103515677","display_name":"Zhengzhi Han","orcid":null},"institutions":[{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhengzhi Han","raw_affiliation_strings":["School of Electronic, Information and Electrical Engineering, Shanghai Jiaotong University, Shanghai 200240, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electronic, Information and Electrical Engineering, Shanghai Jiaotong University, Shanghai 200240, China","institution_ids":["https://openalex.org/I183067930"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5051497320","display_name":"Zhenghua Ma","orcid":"https://orcid.org/0000-0002-4569-6254"},"institutions":[{"id":"https://openalex.org/I4210153482","display_name":"Changzhou University","ror":"https://ror.org/04ymgwq66","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210153482"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhenghua Ma","raw_affiliation_strings":["College of Information and Engineering Science, Changzhou University, Jiangsu 213164, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Information and Engineering Science, Changzhou University, Jiangsu 213164, China","institution_ids":["https://openalex.org/I4210153482"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5036712571"],"corresponding_institution_ids":["https://openalex.org/I183067930","https://openalex.org/I4210153482"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.3598,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.6585834,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"2014","issue":null,"first_page":"1","last_page":"5"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9994000196456909,"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":0.9994000196456909,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9894999861717224,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12592","display_name":"Opinion Dynamics and Social Influence","score":0.9825999736785889,"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/nonlinear-system","display_name":"Nonlinear system","score":0.6573474407196045},{"id":"https://openalex.org/keywords/moment","display_name":"Moment (physics)","score":0.6226081252098083},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.6193361282348633},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.615484893321991},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5300564169883728},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5194656252861023},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5100484490394592},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5082961916923523},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34670114517211914},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.18346932530403137},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1081804633140564}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6573474407196045},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.6226081252098083},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.6193361282348633},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.615484893321991},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5300564169883728},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5194656252861023},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5100484490394592},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5082961916923523},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34670114517211914},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18346932530403137},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1081804633140564},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","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},{"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/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2014/787568","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2014/787568","pdf_url":"https://downloads.hindawi.com/journals/jam/2014/787568.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/1412176997","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jam/1412176997","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:787568","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/JAM/2014/787568.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:ddf0229a458c4826a935675efccb068a","is_oa":true,"landing_page_url":"https://doaj.org/article/ddf0229a458c4826a935675efccb068a","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 2014 (2014)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2014/787568","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2014/787568","pdf_url":"https://downloads.hindawi.com/journals/jam/2014/787568.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/G2787492659","display_name":null,"funder_award_id":"61074003","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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2013110593.pdf","grobid_xml":"https://content.openalex.org/works/W2013110593.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W572539957","https://openalex.org/W1994291702","https://openalex.org/W2013583729","https://openalex.org/W2029946328","https://openalex.org/W2044205615","https://openalex.org/W2057152735","https://openalex.org/W2076859936","https://openalex.org/W2096399107","https://openalex.org/W2119032514","https://openalex.org/W2129916159","https://openalex.org/W2399211344"],"related_works":["https://openalex.org/W1593898832","https://openalex.org/W2756324413","https://openalex.org/W2142048021","https://openalex.org/W2134075948","https://openalex.org/W2383529437","https://openalex.org/W1790223069","https://openalex.org/W2154204858","https://openalex.org/W2081245100","https://openalex.org/W1928921784","https://openalex.org/W4233086528"],"abstract_inverted_index":{"We":[0],"study":[1],"the":[2,6,36,54],"exponential":[3,33],"stability":[4],"of":[5,56],"complex":[7],"dynamical":[8],"network":[9],"described":[10],"by":[11],"differentially":[12],"nonlinear":[13],"equations":[14],"which":[15],"couple":[16],"with":[17,41,46],"time":[18,42],"delay":[19],"and":[20],"stochastic":[21,37],"impulses.":[22],"Some":[23],"sufficient":[24],"conditions":[25],"are":[26],"established":[27],"to":[28,52],"ensure":[29],"p":[30],"th":[31],"moment":[32],"stable":[34],"for":[35],"impulsive":[38],"systems":[39],"(SIS)":[40],"delay.":[43],"An":[44],"example":[45],"its":[47],"numerical":[48],"simulation":[49],"is":[50],"presented":[51],"illustrate":[53],"validation":[55],"main":[57],"results.":[58]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}