{"id":"https://openalex.org/W3215022564","doi":"https://doi.org/10.3390/sym13112231","title":"Periodicity on Neutral-Type Inertial Neural Networks Incorporating Multiple Delays","display_name":"Periodicity on Neutral-Type Inertial Neural Networks Incorporating Multiple Delays","publication_year":2021,"publication_date":"2021-11-22","ids":{"openalex":"https://openalex.org/W3215022564","doi":"https://doi.org/10.3390/sym13112231","mag":"3215022564"},"language":"en","primary_location":{"id":"doi:10.3390/sym13112231","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13112231","pdf_url":"https://www.mdpi.com/2073-8994/13/11/2231/pdf?version=1637572829","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/13/11/2231/pdf?version=1637572829","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101934414","display_name":"Jian Zhang","orcid":"https://orcid.org/0000-0002-1050-6799"},"institutions":[{"id":"https://openalex.org/I16609230","display_name":"Hunan University","ror":"https://ror.org/05htk5m33","country_code":"CN","type":"education","lineage":["https://openalex.org/I16609230"]},{"id":"https://openalex.org/I56934997","display_name":"Changsha University of Science and Technology","ror":"https://ror.org/03yph8055","country_code":"CN","type":"education","lineage":["https://openalex.org/I56934997"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jian Zhang","raw_affiliation_strings":["Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha 410114, China","School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha 410114, China"],"raw_orcid":"https://orcid.org/0000-0002-1050-6799","affiliations":[{"raw_affiliation_string":"Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha 410114, China","institution_ids":["https://openalex.org/I16609230"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha 410114, China","institution_ids":["https://openalex.org/I56934997"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003955906","display_name":"A.O.T. Chang","orcid":"https://orcid.org/0000-0003-3577-4308"},"institutions":[{"id":"https://openalex.org/I16609230","display_name":"Hunan University","ror":"https://ror.org/05htk5m33","country_code":"CN","type":"education","lineage":["https://openalex.org/I16609230"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Ancheng Chang","raw_affiliation_strings":["Department of Mathematics, Hunan University of Information Technology, Changsha 410151, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Hunan University of Information Technology, Changsha 410151, China","institution_ids":["https://openalex.org/I16609230"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101755389","display_name":"Gang Yang","orcid":"https://orcid.org/0000-0002-2732-3622"},"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":"Gang Yang","raw_affiliation_strings":["School of Science, Hunan University of Technology and Business, Changsha 410205, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Science, Hunan University of Technology and Business, Changsha 410205, China","institution_ids":["https://openalex.org/I49934816"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5003955906"],"corresponding_institution_ids":["https://openalex.org/I16609230"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":0.5197,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.68569722,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"13","issue":"11","first_page":"2231","last_page":"2231"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9904999732971191,"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/T10244","display_name":"Chaos control and synchronization","score":0.9812999963760376,"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/artificial-neural-network","display_name":"Artificial neural network","score":0.7579514980316162},{"id":"https://openalex.org/keywords/inertial-frame-of-reference","display_name":"Inertial frame of reference","score":0.7053709626197815},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5708442330360413},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5486963987350464},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5232162475585938},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5152838230133057},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.505852460861206},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.47721487283706665},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.44037970900535583},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.41980451345443726},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3402460217475891},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3297048509120941},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.22604483366012573},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2232629358768463},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.15920734405517578},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.14402687549591064},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.0837254524230957},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.07276797294616699},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.05614790320396423},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.04877936840057373}],"concepts":[{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.7579514980316162},{"id":"https://openalex.org/C173386949","wikidata":"https://www.wikidata.org/wiki/Q192735","display_name":"Inertial frame of reference","level":2,"score":0.7053709626197815},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5708442330360413},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5486963987350464},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5232162475585938},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5152838230133057},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.505852460861206},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.47721487283706665},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.44037970900535583},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.41980451345443726},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3402460217475891},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3297048509120941},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.22604483366012573},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2232629358768463},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.15920734405517578},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.14402687549591064},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0837254524230957},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.07276797294616699},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.05614790320396423},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.04877936840057373},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym13112231","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13112231","pdf_url":"https://www.mdpi.com/2073-8994/13/11/2231/pdf?version=1637572829","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:bfc8df7044f1400a9dd4ed946af501c0","is_oa":true,"landing_page_url":"https://doaj.org/article/bfc8df7044f1400a9dd4ed946af501c0","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":"Symmetry, Vol 13, Iss 11, p 2231 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/13/11/2231/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym13112231","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym13112231","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13112231","pdf_url":"https://www.mdpi.com/2073-8994/13/11/2231/pdf?version=1637572829","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5517599311","display_name":"\u975e\u7ebf\u6027\u79cd\u7fa4\u65f6\u6ede\u5fae\u5206\u7cfb\u7edf\u7684\u591a\u91cd\u7a33\u5b9a\u6027\u7814\u7a76","funder_award_id":"11971076","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":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3215022564.pdf","grobid_xml":"https://content.openalex.org/works/W3215022564.grobid-xml"},"referenced_works_count":79,"referenced_works":["https://openalex.org/W1992652478","https://openalex.org/W1999752002","https://openalex.org/W2005914015","https://openalex.org/W2028027246","https://openalex.org/W2041487791","https://openalex.org/W2079871064","https://openalex.org/W2158844295","https://openalex.org/W2160733420","https://openalex.org/W2563651301","https://openalex.org/W2565214060","https://openalex.org/W2735981021","https://openalex.org/W2754212066","https://openalex.org/W2895674108","https://openalex.org/W2917380072","https://openalex.org/W2925605127","https://openalex.org/W2944331387","https://openalex.org/W2951533199","https://openalex.org/W2953175233","https://openalex.org/W2960545788","https://openalex.org/W2967034841","https://openalex.org/W2968918250","https://openalex.org/W2971840604","https://openalex.org/W2972988067","https://openalex.org/W2976966825","https://openalex.org/W2980525818","https://openalex.org/W2983537235","https://openalex.org/W2990322994","https://openalex.org/W2996581323","https://openalex.org/W2999631501","https://openalex.org/W3000695702","https://openalex.org/W3005544390","https://openalex.org/W3009815657","https://openalex.org/W3010575198","https://openalex.org/W3016683263","https://openalex.org/W3016880264","https://openalex.org/W3017189899","https://openalex.org/W3020992152","https://openalex.org/W3022408125","https://openalex.org/W3022753483","https://openalex.org/W3023113650","https://openalex.org/W3028811719","https://openalex.org/W3029113473","https://openalex.org/W3029252806","https://openalex.org/W3029454707","https://openalex.org/W3031256769","https://openalex.org/W3032667095","https://openalex.org/W3033855827","https://openalex.org/W3034586835","https://openalex.org/W3036672736","https://openalex.org/W3037247126","https://openalex.org/W3044108567","https://openalex.org/W3045686698","https://openalex.org/W3046332558","https://openalex.org/W3081516037","https://openalex.org/W3082314455","https://openalex.org/W3087312110","https://openalex.org/W3087400151","https://openalex.org/W3089308880","https://openalex.org/W3091702267","https://openalex.org/W3093604848","https://openalex.org/W3093633220","https://openalex.org/W3097112189","https://openalex.org/W3111783985","https://openalex.org/W3113322713","https://openalex.org/W3122056492","https://openalex.org/W3129951130","https://openalex.org/W3137770932","https://openalex.org/W3180023929","https://openalex.org/W3185256889","https://openalex.org/W6683267593","https://openalex.org/W6683329787","https://openalex.org/W6740799861","https://openalex.org/W6764033176","https://openalex.org/W6768126455","https://openalex.org/W6770753580","https://openalex.org/W6773373219","https://openalex.org/W6779063355","https://openalex.org/W6783087930","https://openalex.org/W6791357478"],"related_works":["https://openalex.org/W3125070615","https://openalex.org/W1593898832","https://openalex.org/W2142048021","https://openalex.org/W2134075948","https://openalex.org/W4389558692","https://openalex.org/W2164703465","https://openalex.org/W2168383058","https://openalex.org/W2143247663","https://openalex.org/W2050693590","https://openalex.org/W4299682115"],"abstract_inverted_index":{"The":[0,74],"classical":[1],"Hopefield":[2],"neural":[3,29,84],"networks":[4,30],"have":[5],"obvious":[6],"symmetry,":[7],"thus":[8],"the":[9,26,46,56,71,78],"study":[10],"related":[11],"to":[12,69],"its":[13],"dynamic":[14],"behaviors":[15],"has":[16],"been":[17],"widely":[18],"concerned.":[19],"This":[20],"research":[21],"article":[22],"is":[23,59,67],"involved":[24],"with":[25],"neutral-type":[27],"inertial":[28,83],"incorporating":[31],"multiple":[32],"delays.":[33],"By":[34],"making":[35],"an":[36,63],"appropriate":[37],"Lyapunov":[38],"functional,":[39],"one":[40],"novel":[41],"sufficient":[42],"stability":[43,51],"criterion":[44],"for":[45],"existence":[47],"and":[48],"global":[49],"exponential":[50],"of":[52,81],"T-periodic":[53],"solutions":[54],"on":[55],"proposed":[57],"system":[58],"obtained.":[60],"In":[61],"addition,":[62],"instructive":[64],"numerical":[65],"example":[66],"arranged":[68],"support":[70],"present":[72],"approach.":[73],"obtained":[75],"results":[76],"broaden":[77],"application":[79],"range":[80],"neutral-types":[82],"networks.":[85]},"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
