{"id":"https://openalex.org/W2920166147","doi":"https://doi.org/10.4018/978-1-5225-5418-9.ch006","title":"Behavior Studies of Nonlinear Fractional-Order Dynamical Systems Using Bifurcation Diagram","display_name":"Behavior Studies of Nonlinear Fractional-Order Dynamical Systems Using Bifurcation Diagram","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2920166147","doi":"https://doi.org/10.4018/978-1-5225-5418-9.ch006","mag":"2920166147"},"language":"en","primary_location":{"id":"doi:10.4018/978-1-5225-5418-9.ch006","doi":"https://doi.org/10.4018/978-1-5225-5418-9.ch006","is_oa":false,"landing_page_url":"https://doi.org/10.4018/978-1-5225-5418-9.ch006","pdf_url":null,"source":{"id":"https://openalex.org/S4210210208","display_name":"Advances in computer and electrical engineering book series","issn_l":"2327-039X","issn":["2327-039X","2327-0403"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core"],"host_organization":"https://openalex.org/P4310320424","host_organization_name":"IGI Global","host_organization_lineage":["https://openalex.org/P4310320424"],"host_organization_lineage_names":["IGI Global"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Computer and Electrical Engineering","raw_type":"book-chapter"},"volume":{"id":"https://openalex.org/W4238530827","display_name":"Advanced Synchronization Control and Bifurcation of Chaotic Fractional-Order Systems"},"type":"book-chapter","is_traditional":true,"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/A5088862798","display_name":"Karima Rabah","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I98962006","display_name":"University of Skikda","ror":"https://ror.org/02571vj15","country_code":"DZ","type":"education","lineage":["https://openalex.org/I98962006"]}],"countries":["DZ"],"is_corresponding":true,"raw_author_name":"Karima Rabah","raw_affiliation_strings":["20th August 1955 University of Skikda, Algeria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"20th August 1955 University of Skikda, Algeria","institution_ids":["https://openalex.org/I98962006"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5088862798"],"corresponding_institution_ids":["https://openalex.org/I98962006"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"166","last_page":"189"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9286999702453613,"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":0.9286999702453613,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.03909999877214432,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11081","display_name":"Advanced Control Systems Design","score":0.010300000198185444,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/fractional-order-systems","display_name":"fractional-order systems","score":0.8650000095367432},{"id":"https://openalex.org/keywords/chaos-control","display_name":"chaos control","score":0.746999979019165},{"id":"https://openalex.org/keywords/bifurcation-diagrams","display_name":"bifurcation diagrams","score":0.8690000176429749},{"id":"https://openalex.org/keywords/chaotic-dynamics","display_name":"chaotic dynamics","score":0.621999979019165},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"fractional calculus","score":0.7559999823570251},{"id":"https://openalex.org/keywords/sensitivity-to-initial-conditions","display_name":"sensitivity to initial conditions","score":0.8069999814033508},{"id":"https://openalex.org/keywords/feedback-control","display_name":"feedback control","score":0.6029999852180481},{"id":"https://openalex.org/keywords/parameter-dependence","display_name":"parameter dependence","score":0.4880000054836273}],"concepts":[{"id":"https://openalex.org/C86243350","wikidata":"https://www.wikidata.org/wiki/Q2595915","display_name":"Bifurcation diagram","level":4,"score":0.686281144618988},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.6855460405349731},{"id":"https://openalex.org/C95518870","wikidata":"https://www.wikidata.org/wiki/Q49315702","display_name":"Control of chaos","level":5,"score":0.6163074970245361},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6092576384544373},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.5542449951171875},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5283984541893005},{"id":"https://openalex.org/C202759130","wikidata":"https://www.wikidata.org/wiki/Q7662148","display_name":"Synchronization of chaos","level":4,"score":0.5270474553108215},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.4996676445007324},{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.4897048771381378},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4861723780632019},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.4450654685497284},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.33258429169654846},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2957459092140198},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.17327246069908142},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.14542561769485474},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07040292024612427},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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},{"id":"https://openalex.org/C6557445","wikidata":"https://www.wikidata.org/wiki/Q173113","display_name":"Agronomy","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.4018/978-1-5225-5418-9.ch006","doi":"https://doi.org/10.4018/978-1-5225-5418-9.ch006","is_oa":false,"landing_page_url":"https://doi.org/10.4018/978-1-5225-5418-9.ch006","pdf_url":null,"source":{"id":"https://openalex.org/S4210210208","display_name":"Advances in computer and electrical engineering book series","issn_l":"2327-039X","issn":["2327-039X","2327-0403"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core"],"host_organization":"https://openalex.org/P4310320424","host_organization_name":"IGI Global","host_organization_lineage":["https://openalex.org/P4310320424"],"host_organization_lineage_names":["IGI Global"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Computer and Electrical Engineering","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W627854379","https://openalex.org/W1218080659","https://openalex.org/W1517755115","https://openalex.org/W1529051376","https://openalex.org/W1553338987","https://openalex.org/W1584611818","https://openalex.org/W1590893048","https://openalex.org/W1785296378","https://openalex.org/W1791528492","https://openalex.org/W1963675052","https://openalex.org/W1967008192","https://openalex.org/W1969313263","https://openalex.org/W2034011807","https://openalex.org/W2049217659","https://openalex.org/W2103599012","https://openalex.org/W2141394518","https://openalex.org/W2155572235","https://openalex.org/W2317148763","https://openalex.org/W2506586217","https://openalex.org/W2755270292","https://openalex.org/W2799020262"],"related_works":["https://openalex.org/W2130437403","https://openalex.org/W2037545544","https://openalex.org/W2365095326","https://openalex.org/W2007072819","https://openalex.org/W2033033366","https://openalex.org/W2999909382","https://openalex.org/W6996671440","https://openalex.org/W2594566380","https://openalex.org/W2996243624","https://openalex.org/W2377687357"],"abstract_inverted_index":{"Over":[0],"the":[1,7,31,37,44,73,92,125,133,144],"past":[2,93],"decades,":[3],"chaos":[4,106,120],"has":[5,79,108],"stimulated":[6],"interest":[8],"of":[9,18,57,64,102,118,138,146,156],"researchers":[10],"due":[11],"to":[12,30,43,123,132,142],"its":[13],"existence":[14],"in":[15,72,83,112,149,154],"different":[16],"fields":[17,85],"science":[19],"and":[20,86,151,159],"engineering.":[21],"The":[22,67,136],"chaotic":[23,53,104,126,147],"systems":[24,50,148],"are":[25],"characterized":[26],"by":[27],"their":[28,157],"sensitivity":[29],"initial":[32],"conditions.":[33],"This":[34,55],"property":[35],"makes":[36],"system":[38,58],"unpredictable":[39],"long":[40],"term.":[41],"Similar":[42],"integer-order":[45],"differential":[46,49],"systems,":[47],"fractional-order":[48],"can":[51],"exhibit":[52],"behaviors.":[54],"type":[56],"contains":[59],"one":[60],"or":[61,129],"more":[62],"elements":[63],"fractional":[65,68],"order.":[66],"calculus":[69],"is":[70,122,141],"recognized":[71],"early":[74],"seventeenth":[75],"century":[76],"but":[77],"it":[78],"been":[80],"widely":[81],"applied":[82],"many":[84],"with":[87],"intense":[88],"growth":[89],"just":[90],"over":[91],"decades.":[94],"To":[95],"avoid":[96],"troubles":[97],"arising":[98],"from":[99],"unusual":[100],"behaviors":[101],"a":[103,119,161],"system,":[105],"control":[107],"gained":[109],"increasing":[110],"attention":[111],"recent":[113],"years.":[114],"An":[115],"important":[116],"objective":[117],"controller":[121,162],"suppress":[124],"oscillations":[127],"completely":[128],"reduce":[130],"them":[131],"regular":[134],"oscillations.":[135],"goal":[137],"this":[139],"chapter":[140],"present":[143],"evolution":[145],"open":[150],"closed":[152],"loop":[153],"function":[155],"parameters":[158],"designing":[160],"using":[163],"bifurcation":[164],"diagrams.":[165]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2019-03-11T00:00:00"}