{"id":"https://openalex.org/W2040811232","doi":"https://doi.org/10.1142/s0218127404011624","title":"THE DYNAMICS OF SYSTEMS OF COMPLEX NONLINEAR OSCILLATORS: A REVIEW","display_name":"THE DYNAMICS OF SYSTEMS OF COMPLEX NONLINEAR OSCILLATORS: A REVIEW","publication_year":2004,"publication_date":"2004-11-01","ids":{"openalex":"https://openalex.org/W2040811232","doi":"https://doi.org/10.1142/s0218127404011624","mag":"2040811232"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127404011624","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127404011624","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":"review","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/A5030955773","display_name":"Gamal M. Mahmoud","orcid":"https://orcid.org/0000-0003-2673-8065"},"institutions":[{"id":"https://openalex.org/I201726411","display_name":"United Arab Emirates University","ror":"https://ror.org/01km6p862","country_code":"AE","type":"education","lineage":["https://openalex.org/I201726411"]}],"countries":["AE"],"is_corresponding":true,"raw_author_name":"GAMAL M. MAHMOUD","raw_affiliation_strings":["Department of Mathematics &amp; Computer Science, Faculty of Science, United Arab Emirates University, Al Ain P.O. Box 17551, UAE"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics &amp; Computer Science, Faculty of Science, United Arab Emirates University, Al Ain P.O. Box 17551, UAE","institution_ids":["https://openalex.org/I201726411"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5028404620","display_name":"Tassos Bountis","orcid":"https://orcid.org/0000-0002-8103-8152"},"institutions":[{"id":"https://openalex.org/I174878644","display_name":"University of Patras","ror":"https://ror.org/017wvtq80","country_code":"GR","type":"education","lineage":["https://openalex.org/I174878644"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"TASSOS BOUNTIS","raw_affiliation_strings":["Department of Mathematics and Center for Research and Applications for Nonlinear Systems, University of Patras, Patras GR 26500, Greece"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Center for Research and Applications for Nonlinear Systems, University of Patras, Patras GR 26500, Greece","institution_ids":["https://openalex.org/I174878644"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5030955773"],"corresponding_institution_ids":["https://openalex.org/I201726411"],"apc_list":null,"apc_paid":null,"fwci":0.4943,"has_fulltext":false,"cited_by_count":72,"citation_normalized_percentile":{"value":0.64864161,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"14","issue":"11","first_page":"3821","last_page":"3846"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9990000128746033,"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":0.9990000128746033,"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":0.9983000159263611,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9959999918937683,"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/attractor","display_name":"Attractor","score":0.7023041844367981},{"id":"https://openalex.org/keywords/phase-space","display_name":"Phase space","score":0.6891166567802429},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6681251525878906},{"id":"https://openalex.org/keywords/complex-system","display_name":"Complex system","score":0.582068145275116},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.5598734021186829},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.5587201714515686},{"id":"https://openalex.org/keywords/complex-dynamics","display_name":"Complex dynamics","score":0.5113336443901062},{"id":"https://openalex.org/keywords/physical-system","display_name":"Physical system","score":0.4803929924964905},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.46768003702163696},{"id":"https://openalex.org/keywords/control-of-chaos","display_name":"Control of chaos","score":0.4620243012905121},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.45372748374938965},{"id":"https://openalex.org/keywords/brusselator","display_name":"Brusselator","score":0.4453045725822449},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.365736722946167},{"id":"https://openalex.org/keywords/synchronization-of-chaos","display_name":"Synchronization of chaos","score":0.24072998762130737},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.23207876086235046},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22090491652488708},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.18845421075820923},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.13267335295677185},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.12782979011535645}],"concepts":[{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.7023041844367981},{"id":"https://openalex.org/C151342819","wikidata":"https://www.wikidata.org/wiki/Q62542","display_name":"Phase space","level":2,"score":0.6891166567802429},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6681251525878906},{"id":"https://openalex.org/C47822265","wikidata":"https://www.wikidata.org/wiki/Q854457","display_name":"Complex system","level":2,"score":0.582068145275116},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.5598734021186829},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.5587201714515686},{"id":"https://openalex.org/C126701199","wikidata":"https://www.wikidata.org/wiki/Q264224","display_name":"Complex dynamics","level":2,"score":0.5113336443901062},{"id":"https://openalex.org/C116672817","wikidata":"https://www.wikidata.org/wiki/Q1454986","display_name":"Physical system","level":2,"score":0.4803929924964905},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.46768003702163696},{"id":"https://openalex.org/C95518870","wikidata":"https://www.wikidata.org/wiki/Q49315702","display_name":"Control of chaos","level":5,"score":0.4620243012905121},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.45372748374938965},{"id":"https://openalex.org/C14028793","wikidata":"https://www.wikidata.org/wiki/Q906505","display_name":"Brusselator","level":3,"score":0.4453045725822449},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.365736722946167},{"id":"https://openalex.org/C202759130","wikidata":"https://www.wikidata.org/wiki/Q7662148","display_name":"Synchronization of chaos","level":4,"score":0.24072998762130737},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.23207876086235046},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22090491652488708},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.18845421075820923},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.13267335295677185},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.12782979011535645},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127404011624","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127404011624","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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":74,"referenced_works":["https://openalex.org/W186186683","https://openalex.org/W564461737","https://openalex.org/W1496798092","https://openalex.org/W1567277313","https://openalex.org/W1965989821","https://openalex.org/W1967967644","https://openalex.org/W1972138769","https://openalex.org/W1975911021","https://openalex.org/W1984783094","https://openalex.org/W1986177202","https://openalex.org/W2006858638","https://openalex.org/W2008095720","https://openalex.org/W2010538207","https://openalex.org/W2012620638","https://openalex.org/W2012730292","https://openalex.org/W2013578581","https://openalex.org/W2014832198","https://openalex.org/W2016866497","https://openalex.org/W2018021630","https://openalex.org/W2019592819","https://openalex.org/W2021907377","https://openalex.org/W2022072217","https://openalex.org/W2023464234","https://openalex.org/W2026823472","https://openalex.org/W2026977127","https://openalex.org/W2029585432","https://openalex.org/W2036305084","https://openalex.org/W2037543594","https://openalex.org/W2039034656","https://openalex.org/W2042416481","https://openalex.org/W2048196483","https://openalex.org/W2053225475","https://openalex.org/W2054404649","https://openalex.org/W2055463797","https://openalex.org/W2057006750","https://openalex.org/W2060080298","https://openalex.org/W2064120455","https://openalex.org/W2068551947","https://openalex.org/W2070967795","https://openalex.org/W2073400541","https://openalex.org/W2073981166","https://openalex.org/W2077161130","https://openalex.org/W2079388642","https://openalex.org/W2081167612","https://openalex.org/W2082276332","https://openalex.org/W2083791232","https://openalex.org/W2085163390","https://openalex.org/W2088452684","https://openalex.org/W2089876099","https://openalex.org/W2090634581","https://openalex.org/W2091144817","https://openalex.org/W2094133613","https://openalex.org/W2095258853","https://openalex.org/W2103528206","https://openalex.org/W2119596659","https://openalex.org/W2131438242","https://openalex.org/W2152254020","https://openalex.org/W2158180798","https://openalex.org/W2165584546","https://openalex.org/W2169642391","https://openalex.org/W2170999230","https://openalex.org/W2316463358","https://openalex.org/W2326471877","https://openalex.org/W2477244626","https://openalex.org/W2971304175","https://openalex.org/W3094017215","https://openalex.org/W3117619190","https://openalex.org/W4231409469","https://openalex.org/W4237997615","https://openalex.org/W4246335908","https://openalex.org/W4251015067","https://openalex.org/W4294967943","https://openalex.org/W4388311572","https://openalex.org/W4392306314"],"related_works":["https://openalex.org/W628076188","https://openalex.org/W1964949289","https://openalex.org/W1998022189","https://openalex.org/W2020201538","https://openalex.org/W2018375047","https://openalex.org/W2497810705","https://openalex.org/W1546375104","https://openalex.org/W2889373502","https://openalex.org/W2146721763","https://openalex.org/W1964785011"],"abstract_inverted_index":{"Dynamical":[0],"systems":[1,34,95,195],"in":[2,35,145,194,202,241],"the":[3,10,30,71,140,146,152,165,189,225],"real":[4,36],"domain":[5],"are":[6,160,207],"currently":[7],"one":[8],"of":[9,14,19,22,32,45,53,66,73,89,96,122,139,148,155,191,196,214,244],"most":[11],"popular":[12],"areas":[13],"scientific":[15],"study.":[16],"A":[17],"wealth":[18],"new":[20],"phenomena":[21],"bifurcations":[23],"and":[24,93,117,188,205,228,256],"chaos":[25,192],"has":[26],"been":[27,108],"discovered":[28],"concerning":[29],"dynamics":[31],"nonlinear":[33,98,226],"phase":[37,74],"space.":[38],"There":[39],"is,":[40,168],"however,":[41],"a":[42,50,78,212],"wide":[43],"variety":[44],"physical":[46],"problems,":[47],"which,":[48],"from":[49],"mathematical":[51],"point":[52],"view,":[54],"can":[55,131],"be":[56],"more":[57,136],"conveniently":[58],"studied":[59],"using":[60],"complex":[61,68,97,197,215,235],"variables.":[62],"The":[63,119,209],"main":[64],"advantage":[65],"introducing":[67],"variables":[69],"is":[70,144,231],"reduction":[72],"space":[75],"dimensions":[76],"by":[77,129],"half.":[79],"In":[80],"this":[81],"survey,":[82],"we":[83],"shall":[84],"focus":[85],"on":[86,163,179],"such":[87,149,221],"classes":[88],"autonomous,":[90],"parametrically":[91],"excited":[92],"modulated":[94,253],"oscillators.":[99,198],"We":[100,173],"first":[101],"describe":[102],"appropriate":[103],"perturbation":[104],"approaches,":[105],"which":[106,219],"have":[107],"specially":[109],"adapted":[110],"to":[111],"study":[112],"periodic":[113,125,166,182],"solutions,":[114,126,183],"their":[115],"stability":[116,120],"control.":[118],"analysis":[121],"these":[123],"fundamental":[124],"though":[127],"local":[128],"itself,":[130],"yield":[132],"considerable":[133],"information":[134],"about":[135],"global":[137],"properties":[138],"dynamics,":[141],"since":[142],"it":[143],"vicinity":[147],"solutions":[150],"that":[151],"largest":[153],"regions":[154],"regular":[156],"or":[157,171],"chaotic":[158,186],"motion":[159],"observed,":[161],"depending":[162],"whether":[164],"solution":[167],"respectively,":[169],"stable":[170],"unstable.":[172],"then":[174],"summarize":[175],"some":[176],"recent":[177],"studies":[178],"fixed":[180],"points,":[181],"strange":[184],"attractors,":[185],"behavior":[187],"problem":[190],"control":[193],"Some":[199],"important":[200,239],"applications":[201],"physics,":[203,245,250],"mechanics":[204],"engineering":[206],"mentioned.":[208],"connection":[210],"with":[211],"class":[213],"partial":[216],"differential":[217],"equations,":[218],"contains":[220],"famous":[222],"examples,":[223],"as":[224],"Schr\u00f6dinger":[227],"Ginzburg\u2013Landau":[229],"equations":[230,236],"also":[232],"discussed.":[233],"These":[234],"play":[237],"an":[238],"role":[240],"many":[242],"branches":[243],"e.g.":[246],"fluids,":[247,252],"superconductors,":[248],"plasma":[249],"geophysical":[251],"optical":[254],"waves":[255],"electromagnetic":[257],"fields.":[258]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":11},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
