{"id":"https://openalex.org/W2767138906","doi":"https://doi.org/10.1155/2017/5982365","title":"Exponential Synchronization of a Class of <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\"><mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:math>-Coupled Complex Partial Differential Systems with Time-Varying Delay","display_name":"Exponential Synchronization of a Class of <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\"><mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:math>-Coupled Complex Partial Differential Systems with Time-Varying Delay","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2767138906","doi":"https://doi.org/10.1155/2017/5982365","mag":"2767138906"},"language":"en","primary_location":{"id":"doi:10.1155/2017/5982365","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2017/5982365","pdf_url":"http://downloads.hindawi.com/journals/complexity/2017/5982365.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"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":"Complexity","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"http://downloads.hindawi.com/journals/complexity/2017/5982365.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5085418346","display_name":"Wenhua Xia","orcid":"https://orcid.org/0000-0003-2063-1929"},"institutions":[{"id":"https://openalex.org/I27688046","display_name":"Hunan Institute of Engineering","ror":"https://ror.org/03zj2rn70","country_code":"CN","type":"education","lineage":["https://openalex.org/I27688046"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wenhua Xia","raw_affiliation_strings":["College of Science, Hunan Institute of Engineering, Hunan 411104, China"],"affiliations":[{"raw_affiliation_string":"College of Science, Hunan Institute of Engineering, Hunan 411104, China","institution_ids":["https://openalex.org/I27688046"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078160022","display_name":"Yiping Luo","orcid":"https://orcid.org/0000-0002-2963-7270"},"institutions":[{"id":"https://openalex.org/I27688046","display_name":"Hunan Institute of Engineering","ror":"https://ror.org/03zj2rn70","country_code":"CN","type":"education","lineage":["https://openalex.org/I27688046"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yiping Luo","raw_affiliation_strings":["College of Science, Hunan Institute of Engineering, Hunan 411104, China"],"affiliations":[{"raw_affiliation_string":"College of Science, Hunan Institute of Engineering, Hunan 411104, China","institution_ids":["https://openalex.org/I27688046"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029285106","display_name":"Bifeng Zhou","orcid":"https://orcid.org/0000-0003-2245-6722"},"institutions":[{"id":"https://openalex.org/I49934816","display_name":"Hunan University of Technology","ror":"https://ror.org/04j3vr751","country_code":"CN","type":"education","lineage":["https://openalex.org/I49934816"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bifeng Zhou","raw_affiliation_strings":["Hunan Electrical College of Technology, Hunan 411101, China"],"affiliations":[{"raw_affiliation_string":"Hunan Electrical College of Technology, Hunan 411101, China","institution_ids":["https://openalex.org/I49934816"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100654860","display_name":"Guanghui Liu","orcid":"https://orcid.org/0000-0002-4170-4552"},"institutions":[{"id":"https://openalex.org/I27688046","display_name":"Hunan Institute of Engineering","ror":"https://ror.org/03zj2rn70","country_code":"CN","type":"education","lineage":["https://openalex.org/I27688046"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guanghui Liu","raw_affiliation_strings":["College of Science, Hunan Institute of Engineering, Hunan 411104, China"],"affiliations":[{"raw_affiliation_string":"College of Science, Hunan Institute of Engineering, Hunan 411104, China","institution_ids":["https://openalex.org/I27688046"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5078160022"],"corresponding_institution_ids":["https://openalex.org/I27688046"],"apc_list":{"value":2300,"currency":"USD","value_usd":2300},"apc_paid":{"value":2300,"currency":"USD","value_usd":2300},"fwci":0.4375,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.68742602,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"2017","issue":null,"first_page":"1","last_page":"9"},"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9987000226974487,"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/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9926000237464905,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5932114124298096},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.471405029296875},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.4525711238384247},{"id":"https://openalex.org/keywords/synchronization","display_name":"Synchronization (alternating current)","score":0.4417009949684143},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4246745705604553},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.30501824617385864},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.22094887495040894},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.16629359126091003},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1268472671508789},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.12325623631477356}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5932114124298096},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.471405029296875},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.4525711238384247},{"id":"https://openalex.org/C2778562939","wikidata":"https://www.wikidata.org/wiki/Q1298791","display_name":"Synchronization (alternating current)","level":3,"score":0.4417009949684143},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4246745705604553},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.30501824617385864},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.22094887495040894},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.16629359126091003},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1268472671508789},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.12325623631477356}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1155/2017/5982365","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2017/5982365","pdf_url":"http://downloads.hindawi.com/journals/complexity/2017/5982365.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"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":"Complexity","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:de14dfd14db94d208106f2d1bf085511","is_oa":true,"landing_page_url":"https://doaj.org/article/de14dfd14db94d208106f2d1bf085511","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Complexity, Vol 2017 (2017)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2017/5982365","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2017/5982365","pdf_url":"http://downloads.hindawi.com/journals/complexity/2017/5982365.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"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":"Complexity","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1436023622","display_name":null,"funder_award_id":"11372107","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2087396116","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3317480652","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3556998877","display_name":null,"funder_award_id":"2017JJ5011","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5994120800","display_name":null,"funder_award_id":"Natural","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6178674484","display_name":null,"funder_award_id":"2017JJ4004","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/W2767138906.pdf","grobid_xml":"https://content.openalex.org/works/W2767138906.grobid-xml"},"referenced_works_count":42,"referenced_works":["https://openalex.org/W1519488445","https://openalex.org/W1965795656","https://openalex.org/W1975569524","https://openalex.org/W1983786160","https://openalex.org/W1997741068","https://openalex.org/W2019091709","https://openalex.org/W2031360297","https://openalex.org/W2031988165","https://openalex.org/W2037035296","https://openalex.org/W2037521841","https://openalex.org/W2038524744","https://openalex.org/W2038638422","https://openalex.org/W2041833126","https://openalex.org/W2042943502","https://openalex.org/W2049034415","https://openalex.org/W2059707615","https://openalex.org/W2060008649","https://openalex.org/W2060256854","https://openalex.org/W2062308970","https://openalex.org/W2062692785","https://openalex.org/W2063012440","https://openalex.org/W2075049885","https://openalex.org/W2075930670","https://openalex.org/W2077329278","https://openalex.org/W2085465150","https://openalex.org/W2086987978","https://openalex.org/W2098974515","https://openalex.org/W2109952733","https://openalex.org/W2148606196","https://openalex.org/W2164727176","https://openalex.org/W2165924259","https://openalex.org/W2172433224","https://openalex.org/W2309551618","https://openalex.org/W2312234994","https://openalex.org/W2323993786","https://openalex.org/W2469091728","https://openalex.org/W2478973922","https://openalex.org/W2502146633","https://openalex.org/W2549940866","https://openalex.org/W2552912013","https://openalex.org/W2564401762","https://openalex.org/W4255882176"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644","https://openalex.org/W2042127053"],"abstract_inverted_index":{"This":[0],"paper":[1,88],"is":[2,30,51],"concerned":[3],"with":[4,20],"the":[5,28,33,55,59,63,83,91],"exponential":[6,56],"synchronization":[7,24,57],"for":[8],"a":[9,44],"class":[10],"of":[11,27,58,86],"<mml:math":[12,34],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[13,35],"id=\"M2\"><mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:math>-coupled":[14],"complex":[15],"partial":[16],"differential":[17],"systems":[18],"(PDSs)":[19],"time-varying":[21],"delay.":[22],"The":[23,71],"error":[25],"dynamic":[26],"PDSs":[29],"defined":[31],"in":[32,82],"id=\"M3\"><mml:mrow><mml:mi>q</mml:mi></mml:mrow></mml:math>-dimensional":[36],"spatial":[37],"domain.":[38],"To":[39],"achieve":[40],"synchronization,":[41],"we":[42],"added":[43],"linear":[45],"feedback":[46],"controller.":[47],"A":[48],"sufficient":[49],"condition":[50],"derived":[52],"to":[53,89],"ensure":[54],"proposed":[60,72,92],"networks":[61],"using":[62],"Lyapunov\u2013Krasovskii":[64],"stability":[65],"approach":[66],"and":[67],"matrix":[68],"inequality":[69],"technology.":[70],"system":[73],"has":[74],"broad":[75],"applications.":[76],"Two":[77],"example":[78],"applications":[79],"are":[80],"presented":[81],"final":[84],"section":[85],"this":[87],"verify":[90],"theoretical":[93],"result.":[94]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2026-03-18T14:38:29.013473","created_date":"2017-11-10T00:00:00"}