{"id":"https://openalex.org/W4318999661","doi":"https://doi.org/10.3390/axioms12020157","title":"Hybrid Projective Synchronization of Fractional-Order Extended Hindmarsh\u2013Rose Neurons with Hidden Attractors","display_name":"Hybrid Projective Synchronization of Fractional-Order Extended Hindmarsh\u2013Rose Neurons with Hidden Attractors","publication_year":2023,"publication_date":"2023-02-02","ids":{"openalex":"https://openalex.org/W4318999661","doi":"https://doi.org/10.3390/axioms12020157"},"language":"en","primary_location":{"id":"doi:10.3390/axioms12020157","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12020157","pdf_url":"https://www.mdpi.com/2075-1680/12/2/157/pdf?version=1675331449","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/12/2/157/pdf?version=1675331449","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5007306404","display_name":"Xuerong Shi","orcid":"https://orcid.org/0000-0002-7727-3678"},"institutions":[{"id":"https://openalex.org/I4210141689","display_name":"Yancheng Teachers University","ror":"https://ror.org/042k5fe81","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210141689"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xuerong Shi","raw_affiliation_strings":["School of Mathematics and Statistics, Yancheng Teachers University, Yancheng 224002, China"],"raw_orcid":"https://orcid.org/0000-0002-7727-3678","affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Yancheng Teachers University, Yancheng 224002, China","institution_ids":["https://openalex.org/I4210141689"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050677757","display_name":"Zuolei Wang","orcid":"https://orcid.org/0000-0002-3442-2717"},"institutions":[{"id":"https://openalex.org/I4210141689","display_name":"Yancheng Teachers University","ror":"https://ror.org/042k5fe81","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210141689"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zuolei Wang","raw_affiliation_strings":["School of Mathematics and Statistics, Yancheng Teachers University, Yancheng 224002, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Yancheng Teachers University, Yancheng 224002, China","institution_ids":["https://openalex.org/I4210141689"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5050677757"],"corresponding_institution_ids":["https://openalex.org/I4210141689"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.2929,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.48174079,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"12","issue":"2","first_page":"157","last_page":"157"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11513","display_name":"stochastic dynamics and bifurcation","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T11513","display_name":"stochastic dynamics and bifurcation","score":1.0,"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"}},{"id":"https://openalex.org/T10581","display_name":"Neural dynamics and brain function","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9976000189781189,"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/attractor","display_name":"Attractor","score":0.795882523059845},{"id":"https://openalex.org/keywords/biological-neuron-model","display_name":"Biological neuron model","score":0.7619192600250244},{"id":"https://openalex.org/keywords/neuron","display_name":"Neuron","score":0.606586754322052},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5326793789863586},{"id":"https://openalex.org/keywords/synchronization","display_name":"Synchronization (alternating current)","score":0.5280029773712158},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.48629888892173767},{"id":"https://openalex.org/keywords/equilibrium-point","display_name":"Equilibrium point","score":0.48344144225120544},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.4393404424190521},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4381510019302368},{"id":"https://openalex.org/keywords/rose","display_name":"Rose (mathematics)","score":0.4277384281158447},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3826998174190521},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.2581809461116791},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2280176281929016},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2236531674861908},{"id":"https://openalex.org/keywords/neuroscience","display_name":"Neuroscience","score":0.1553342044353485},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.09453317523002625},{"id":"https://openalex.org/keywords/psychology","display_name":"Psychology","score":0.08086153864860535},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07650646567344666},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.07243779301643372},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.0709998607635498}],"concepts":[{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.795882523059845},{"id":"https://openalex.org/C186565885","wikidata":"https://www.wikidata.org/wiki/Q1651163","display_name":"Biological neuron model","level":3,"score":0.7619192600250244},{"id":"https://openalex.org/C2778794669","wikidata":"https://www.wikidata.org/wiki/Q43054","display_name":"Neuron","level":2,"score":0.606586754322052},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5326793789863586},{"id":"https://openalex.org/C2778562939","wikidata":"https://www.wikidata.org/wiki/Q1298791","display_name":"Synchronization (alternating current)","level":3,"score":0.5280029773712158},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.48629888892173767},{"id":"https://openalex.org/C94766913","wikidata":"https://www.wikidata.org/wiki/Q1530271","display_name":"Equilibrium point","level":3,"score":0.48344144225120544},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.4393404424190521},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4381510019302368},{"id":"https://openalex.org/C2778335665","wikidata":"https://www.wikidata.org/wiki/Q1155211","display_name":"Rose (mathematics)","level":2,"score":0.4277384281158447},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3826998174190521},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.2581809461116791},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2280176281929016},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2236531674861908},{"id":"https://openalex.org/C169760540","wikidata":"https://www.wikidata.org/wiki/Q207011","display_name":"Neuroscience","level":1,"score":0.1553342044353485},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.09453317523002625},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.08086153864860535},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07650646567344666},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.07243779301643372},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0709998607635498},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms12020157","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12020157","pdf_url":"https://www.mdpi.com/2075-1680/12/2/157/pdf?version=1675331449","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:e9af8daae97048e5873b644127c22e2c","is_oa":true,"landing_page_url":"https://doaj.org/article/e9af8daae97048e5873b644127c22e2c","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":"Axioms, Vol 12, Iss 2, p 157 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/12/2/157/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms12020157","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":"Axioms","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms12020157","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12020157","pdf_url":"https://www.mdpi.com/2075-1680/12/2/157/pdf?version=1675331449","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2117326584","display_name":null,"funder_award_id":"11872327","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5560655810","display_name":null,"funder_award_id":"20KJA190001","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/W4318999661.pdf","grobid_xml":"https://content.openalex.org/works/W4318999661.grobid-xml"},"referenced_works_count":50,"referenced_works":["https://openalex.org/W1837191798","https://openalex.org/W1968435495","https://openalex.org/W1978870897","https://openalex.org/W1995992845","https://openalex.org/W2031639690","https://openalex.org/W2042316744","https://openalex.org/W2046424015","https://openalex.org/W2081752958","https://openalex.org/W2089021189","https://openalex.org/W2163057446","https://openalex.org/W2164653071","https://openalex.org/W2320160082","https://openalex.org/W2339554881","https://openalex.org/W2522272408","https://openalex.org/W2527443073","https://openalex.org/W2553383303","https://openalex.org/W2747903407","https://openalex.org/W2792820938","https://openalex.org/W2895424216","https://openalex.org/W2905254681","https://openalex.org/W2918982958","https://openalex.org/W2919826067","https://openalex.org/W2949733944","https://openalex.org/W2964358018","https://openalex.org/W2970878972","https://openalex.org/W2973336894","https://openalex.org/W2979969993","https://openalex.org/W2985127177","https://openalex.org/W3002247996","https://openalex.org/W3002437158","https://openalex.org/W3014491148","https://openalex.org/W3014957683","https://openalex.org/W3047826196","https://openalex.org/W3088401711","https://openalex.org/W3110426581","https://openalex.org/W3120165686","https://openalex.org/W3194505184","https://openalex.org/W3203152876","https://openalex.org/W4220673218","https://openalex.org/W4221089166","https://openalex.org/W4223488819","https://openalex.org/W4224121954","https://openalex.org/W4280530475","https://openalex.org/W4285900111","https://openalex.org/W6642280536","https://openalex.org/W6671272107","https://openalex.org/W6683753088","https://openalex.org/W6743471670","https://openalex.org/W6786599339","https://openalex.org/W6789176868"],"related_works":["https://openalex.org/W3011334989","https://openalex.org/W4388853539","https://openalex.org/W2730255634","https://openalex.org/W3178259930","https://openalex.org/W1769982787","https://openalex.org/W3184949856","https://openalex.org/W3035839890","https://openalex.org/W4387066885","https://openalex.org/W4281997648","https://openalex.org/W3099906890"],"abstract_inverted_index":{"In":[0,88],"view":[1],"of":[2,5,35,49,57,79,101,108],"the":[3,20,36,47,58,77,80,90,98,106],"diversity":[4],"stimulated":[6],"current":[7],"that":[8],"neurons":[9,60],"may":[10],"experience,":[11],"an":[12],"extended":[13],"Hindmarsh\u2013Rose":[14],"neuron":[15,23,38,51,102,109],"model":[16,39],"is":[17,29,83],"proposed":[18,59],"and":[19,46,63,104],"corresponding":[21],"fractional-order":[22,50],"model,":[24],"with":[25],"no":[26],"equilibrium":[27],"point,":[28],"depicted.":[30],"Additionally,":[31],"various":[32],"hidden":[33],"attractors":[34],"addressed":[37],"are":[40,61,65],"analyzed":[41],"by":[42,67],"changing":[43],"system":[44,103],"parameters":[45],"order":[48],"system.":[52],"Furthermore,":[53],"hybrid":[54],"projective":[55],"synchronizations":[56],"investigated":[62],"schemes":[64],"obtained":[66],"designing":[68],"suitable":[69],"controllers":[70],"according":[71],"to":[72],"fractional":[73],"stability":[74],"theory.":[75],"Besides,":[76],"validity":[78],"theoretical":[81],"results":[82,92],"verified":[84],"through":[85],"numerical":[86],"simulations.":[87],"short,":[89],"research":[91],"have":[93],"potential":[94],"application":[95],"in":[96],"revealing":[97],"dynamical":[99],"behaviors":[100,107],"controlling":[105],"into":[110],"certain":[111],"status.":[112]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2026-06-15T08:34:33.830935","created_date":"2025-10-10T00:00:00"}