{"id":"https://openalex.org/W2090617101","doi":"https://doi.org/10.1142/s021812740501234x","title":"CONTROLLING CHAOS TO A CLASS OF PDEs BY APPLYING INVARIANT MANIFOLD AND STRUCTURE STABILITY THEORY","display_name":"CONTROLLING CHAOS TO A CLASS OF PDEs BY APPLYING INVARIANT MANIFOLD AND STRUCTURE STABILITY THEORY","publication_year":2005,"publication_date":"2005-02-01","ids":{"openalex":"https://openalex.org/W2090617101","doi":"https://doi.org/10.1142/s021812740501234x","mag":"2090617101"},"language":"en","primary_location":{"id":"doi:10.1142/s021812740501234x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021812740501234x","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/A5101931567","display_name":"Yi Zhao","orcid":"https://orcid.org/0009-0008-3957-7591"},"institutions":[{"id":"https://openalex.org/I157773358","display_name":"Sun Yat-sen University","ror":"https://ror.org/0064kty71","country_code":"CN","type":"education","lineage":["https://openalex.org/I157773358"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"YI ZHAO","raw_affiliation_strings":["Department of Mathematics, Zhongshan University, Guangzhou 510275, P. R. China","Department of Mathematics , Zhongshan University , Guangzhou, 510275, P.R.China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Zhongshan University, Guangzhou 510275, P. R. China","institution_ids":["https://openalex.org/I157773358"]},{"raw_affiliation_string":"Department of Mathematics , Zhongshan University , Guangzhou, 510275, P.R.China","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5085695339","display_name":"S. H. Hou","orcid":"https://orcid.org/0000-0003-3537-9105"},"institutions":[{"id":"https://openalex.org/I14243506","display_name":"Hong Kong Polytechnic University","ror":"https://ror.org/0030zas98","country_code":"HK","type":"education","lineage":["https://openalex.org/I14243506"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"S. H. HOU","raw_affiliation_strings":["Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, China","Department of Applied Mathematics, The Hong Kong Polytechnic University , Hong Kong, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, China","institution_ids":["https://openalex.org/I14243506"]},{"raw_affiliation_string":"Department of Applied Mathematics, The Hong Kong Polytechnic University , Hong Kong, China","institution_ids":["https://openalex.org/I14243506"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.7419,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.71491843,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"15","issue":"02","first_page":"533","last_page":"546"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9975000023841858,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9975000023841858,"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/T10244","display_name":"Chaos control and synchronization","score":0.9962999820709229,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9962000250816345,"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":0.8401134014129639},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7251089215278625},{"id":"https://openalex.org/keywords/lyapunov-exponent","display_name":"Lyapunov exponent","score":0.7034496068954468},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.6135952472686768},{"id":"https://openalex.org/keywords/invariant-manifold","display_name":"Invariant manifold","score":0.594673752784729},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.5662351846694946},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.5363408923149109},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5344464182853699},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.4811721742153168},{"id":"https://openalex.org/keywords/synchronization-of-chaos","display_name":"Synchronization of chaos","score":0.46589338779449463},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.45904630422592163},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.44984883069992065},{"id":"https://openalex.org/keywords/control-of-chaos","display_name":"Control of chaos","score":0.43652141094207764},{"id":"https://openalex.org/keywords/center-manifold","display_name":"Center manifold","score":0.42609351873397827},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4240760803222656},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4105511009693146},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4002628028392792},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.37365150451660156},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.19065186381340027},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.18954059481620789},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.15694624185562134},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11028867959976196},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.09035450220108032},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.08101031184196472},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07788664102554321}],"concepts":[{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.8401134014129639},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7251089215278625},{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.7034496068954468},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.6135952472686768},{"id":"https://openalex.org/C20483540","wikidata":"https://www.wikidata.org/wiki/Q4200516","display_name":"Invariant manifold","level":2,"score":0.594673752784729},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.5662351846694946},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.5363408923149109},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5344464182853699},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.4811721742153168},{"id":"https://openalex.org/C202759130","wikidata":"https://www.wikidata.org/wiki/Q7662148","display_name":"Synchronization of chaos","level":4,"score":0.46589338779449463},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.45904630422592163},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.44984883069992065},{"id":"https://openalex.org/C95518870","wikidata":"https://www.wikidata.org/wiki/Q49315702","display_name":"Control of chaos","level":5,"score":0.43652141094207764},{"id":"https://openalex.org/C74774103","wikidata":"https://www.wikidata.org/wiki/Q4504202","display_name":"Center manifold","level":5,"score":0.42609351873397827},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4240760803222656},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4105511009693146},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4002628028392792},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.37365150451660156},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.19065186381340027},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.18954059481620789},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15694624185562134},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11028867959976196},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.09035450220108032},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.08101031184196472},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07788664102554321},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s021812740501234x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021812740501234x","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"},{"id":"pmh:oai:ira.lib.polyu.edu.hk:10397/14083","is_oa":false,"landing_page_url":"http://hdl.handle.net/10397/14083","pdf_url":null,"source":{"id":"https://openalex.org/S4306400205","display_name":"PolyU Institutional Research Archive (Hong Kong Polytechnic University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I14243506","host_organization_name":"Hong Kong Polytechnic University","host_organization_lineage":["https://openalex.org/I14243506"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal/Magazine Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W105648097","https://openalex.org/W424045364","https://openalex.org/W1594759473","https://openalex.org/W1972122946","https://openalex.org/W1975689102","https://openalex.org/W1981469439","https://openalex.org/W1983043808","https://openalex.org/W1987205119","https://openalex.org/W1992562200","https://openalex.org/W2009116784","https://openalex.org/W2013767620","https://openalex.org/W2013921840","https://openalex.org/W2017908968","https://openalex.org/W2020598201","https://openalex.org/W2025795445","https://openalex.org/W2027648943","https://openalex.org/W2038143838","https://openalex.org/W2058791052","https://openalex.org/W2060812972","https://openalex.org/W2061974529","https://openalex.org/W2062106158","https://openalex.org/W2062908485","https://openalex.org/W2063142053","https://openalex.org/W2066976366","https://openalex.org/W2067306155","https://openalex.org/W2104241324","https://openalex.org/W2106405308","https://openalex.org/W2146050018","https://openalex.org/W2158567118","https://openalex.org/W2529672911","https://openalex.org/W2696718700"],"related_works":["https://openalex.org/W2392447668","https://openalex.org/W4226388829","https://openalex.org/W2780226079","https://openalex.org/W2070844282","https://openalex.org/W1983594265","https://openalex.org/W1496745782","https://openalex.org/W1491593166","https://openalex.org/W2298939083","https://openalex.org/W1602288242","https://openalex.org/W1581278046"],"abstract_inverted_index":{"In":[0,50],"this":[1],"paper,":[2],"we":[3],"are":[4],"concerned":[5],"with":[6],"the":[7,33,36,59,63,66,74],"chaotic":[8,60],"behavior":[9,61],"of":[10,13,23,44,62,77],"a":[11,45],"class":[12],"control":[14],"systems":[15],"described":[16],"by":[17,72],"partial":[18],"differential":[19],"equations.":[20],"By":[21],"means":[22],"finite":[24,46,80],"dimensional":[25,47,81],"output":[26],"feedback":[27],"control,":[28],"it":[29],"is":[30,39,54],"shown":[31],"that":[32,43,58],"flow":[34,64],"on":[35,65],"global":[37,67],"attractor":[38,68],"topologically":[40],"equivalent":[41],"to":[42,56],"difference":[48,82],"system.":[49,83],"addition,":[51],"an":[52,78],"example":[53],"given":[55],"illustrate":[57],"can":[69],"be":[70],"determined":[71],"computing":[73],"Lyapunov":[75],"exponent":[76],"associated":[79]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
