{"id":"https://openalex.org/W1998049234","doi":"https://doi.org/10.1142/s0218127402005534","title":"\"MIDDLE\" PERIODIC ORBIT AND ITS APPLICATION TO CHAOS CONTROL","display_name":"\"MIDDLE\" PERIODIC ORBIT AND ITS APPLICATION TO CHAOS CONTROL","publication_year":2002,"publication_date":"2002-08-01","ids":{"openalex":"https://openalex.org/W1998049234","doi":"https://doi.org/10.1142/s0218127402005534","mag":"1998049234"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127402005534","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127402005534","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","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/A5101672109","display_name":"Yang Ling","orcid":"https://orcid.org/0000-0001-7449-0266"},"institutions":[{"id":"https://openalex.org/I113940042","display_name":"Shanghai University","ror":"https://ror.org/006teas31","country_code":"CN","type":"education","lineage":["https://openalex.org/I113940042"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"LING YANG","raw_affiliation_strings":["Department of Mathematics, Shanghai University, Shanghai 201800, China","Department of Mathematics, Suzhou University, Jiangsu 215006, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shanghai University, Shanghai 201800, China","institution_ids":["https://openalex.org/I113940042"]},{"raw_affiliation_string":"Department of Mathematics, Suzhou University, Jiangsu 215006, China","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112107398","display_name":"Zengrong Liu","orcid":null},"institutions":[{"id":"https://openalex.org/I113940042","display_name":"Shanghai University","ror":"https://ror.org/006teas31","country_code":"CN","type":"education","lineage":["https://openalex.org/I113940042"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"ZENGRONG LIU","raw_affiliation_strings":["Department of Mathematics, Shanghai University, Shanghai 201800, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shanghai University, Shanghai 201800, China","institution_ids":["https://openalex.org/I113940042"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101165933","display_name":"Yongai Zheng","orcid":null},"institutions":[{"id":"https://openalex.org/I113940042","display_name":"Shanghai University","ror":"https://ror.org/006teas31","country_code":"CN","type":"education","lineage":["https://openalex.org/I113940042"]},{"id":"https://openalex.org/I78978612","display_name":"Yangzhou University","ror":"https://ror.org/03tqb8s11","country_code":"CN","type":"education","lineage":["https://openalex.org/I78978612"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"YONGAI ZHENG","raw_affiliation_strings":["Department of Mathematics, Shanghai University, Shanghai 201800, China","Department of Mathematics, Yangzhou University, Jiangsu 225002, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shanghai University, Shanghai 201800, China","institution_ids":["https://openalex.org/I113940042"]},{"raw_affiliation_string":"Department of Mathematics, Yangzhou University, Jiangsu 225002, China","institution_ids":["https://openalex.org/I78978612"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5293,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.66452098,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"12","issue":"08","first_page":"1869","last_page":"1876"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9988999962806702,"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/T10244","display_name":"Chaos control and synchronization","score":0.9988999962806702,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9919000267982483,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9909999966621399,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.7645468711853027},{"id":"https://openalex.org/keywords/topological-entropy","display_name":"Topological entropy","score":0.7481929659843445},{"id":"https://openalex.org/keywords/orbit","display_name":"Orbit (dynamics)","score":0.7084560990333557},{"id":"https://openalex.org/keywords/periodic-orbits","display_name":"Periodic orbits","score":0.6912106275558472},{"id":"https://openalex.org/keywords/heteroclinic-orbit","display_name":"Heteroclinic orbit","score":0.6894379258155823},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.6276461482048035},{"id":"https://openalex.org/keywords/control-of-chaos","display_name":"Control of chaos","score":0.6024885177612305},{"id":"https://openalex.org/keywords/crisis","display_name":"Crisis","score":0.5468959808349609},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.515110194683075},{"id":"https://openalex.org/keywords/periodic-point","display_name":"Periodic point","score":0.5058943629264832},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.424490749835968},{"id":"https://openalex.org/keywords/elliptic-orbit","display_name":"Elliptic orbit","score":0.41109126806259155},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.40849196910858154},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3335736393928528},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.30876192450523376},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2702789306640625},{"id":"https://openalex.org/keywords/synchronization-of-chaos","display_name":"Synchronization of chaos","score":0.25179338455200195},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.22484347224235535},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.2142513394355774},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.15602612495422363},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.15554699301719666},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.1286458969116211},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08364319801330566},{"id":"https://openalex.org/keywords/homoclinic-orbit","display_name":"Homoclinic orbit","score":0.061792999505996704}],"concepts":[{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.7645468711853027},{"id":"https://openalex.org/C2780350623","wikidata":"https://www.wikidata.org/wiki/Q3055355","display_name":"Topological entropy","level":2,"score":0.7481929659843445},{"id":"https://openalex.org/C196644772","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Orbit (dynamics)","level":2,"score":0.7084560990333557},{"id":"https://openalex.org/C2984157986","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Periodic orbits","level":2,"score":0.6912106275558472},{"id":"https://openalex.org/C184481792","wikidata":"https://www.wikidata.org/wiki/Q1992087","display_name":"Heteroclinic orbit","level":5,"score":0.6894379258155823},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.6276461482048035},{"id":"https://openalex.org/C95518870","wikidata":"https://www.wikidata.org/wiki/Q49315702","display_name":"Control of chaos","level":5,"score":0.6024885177612305},{"id":"https://openalex.org/C78302928","wikidata":"https://www.wikidata.org/wiki/Q5185947","display_name":"Crisis","level":4,"score":0.5468959808349609},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.515110194683075},{"id":"https://openalex.org/C46581059","wikidata":"https://www.wikidata.org/wiki/Q116301","display_name":"Periodic point","level":2,"score":0.5058943629264832},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.424490749835968},{"id":"https://openalex.org/C173990265","wikidata":"https://www.wikidata.org/wiki/Q2268240","display_name":"Elliptic orbit","level":2,"score":0.41109126806259155},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.40849196910858154},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3335736393928528},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.30876192450523376},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2702789306640625},{"id":"https://openalex.org/C202759130","wikidata":"https://www.wikidata.org/wiki/Q7662148","display_name":"Synchronization of chaos","level":4,"score":0.25179338455200195},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.22484347224235535},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.2142513394355774},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.15602612495422363},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.15554699301719666},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.1286458969116211},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08364319801330566},{"id":"https://openalex.org/C200581526","wikidata":"https://www.wikidata.org/wiki/Q690494","display_name":"Homoclinic orbit","level":4,"score":0.061792999505996704},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127402005534","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127402005534","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","score":0.5899999737739563,"id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1991746188","https://openalex.org/W2001299891","https://openalex.org/W2033682634","https://openalex.org/W2038152941","https://openalex.org/W2040935283","https://openalex.org/W2055660413","https://openalex.org/W2067989167","https://openalex.org/W2479660560","https://openalex.org/W4237305881","https://openalex.org/W4248796009","https://openalex.org/W4251015067"],"related_works":["https://openalex.org/W1977191517","https://openalex.org/W2186586439","https://openalex.org/W2147240237","https://openalex.org/W2092360752","https://openalex.org/W2785433934","https://openalex.org/W2073732813","https://openalex.org/W129814329","https://openalex.org/W1984913125","https://openalex.org/W2062519455","https://openalex.org/W1998049234"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"a":[3,11,36,40],"new":[4],"method,":[5,75],"by":[6,53],"which":[7],"any":[8,18],"point":[9,34],"in":[10,35,61],"chaotic":[12,37],"attractor":[13,38],"can":[14,50],"be":[15,51],"guided":[16],"to":[17,30,39,80,95],"target":[19,44],"periodic":[20,26,66],"orbit,":[21,45],"is":[22,28,68,77,93],"proposed.":[23],"The":[24,58],"\"Middle\"":[25,65],"orbit":[27,67],"used":[29,94],"lead":[31],"an":[32],"initial":[33],"neighborhood":[41],"of":[42,72,83,87],"the":[43,54,62,73,81,84,88,97],"and":[46,76],"then":[47],"controlling":[48],"chaos":[49],"achieved":[52],"improved":[55],"OGY":[56,74],"method.":[57],"time":[59],"needed":[60],"method":[63],"using":[64],"less":[69],"than":[70],"that":[71],"inversely":[78],"proportional":[79],"square":[82],"topological":[85],"entropy":[86],"given":[89],"map.":[90],"An":[91],"example":[92],"illustrate":[96],"results.":[98]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}