{"id":"https://openalex.org/W2562411014","doi":"https://doi.org/10.1142/s0218127416502229","title":"Dynamical Analysis and Circuit Simulation of a New Fractional-Order Hyperchaotic System and Its Discretization","display_name":"Dynamical Analysis and Circuit Simulation of a New Fractional-Order Hyperchaotic System and Its Discretization","publication_year":2016,"publication_date":"2016-12-15","ids":{"openalex":"https://openalex.org/W2562411014","doi":"https://doi.org/10.1142/s0218127416502229","mag":"2562411014"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127416502229","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127416502229","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/A5100784242","display_name":"A\u200e. \u200eM\u200e. \u200eA\u200e. El-Sayed","orcid":"https://orcid.org/0000-0001-7092-7950"},"institutions":[{"id":"https://openalex.org/I84524832","display_name":"Alexandria University","ror":"https://ror.org/00mzz1w90","country_code":"EG","type":"education","lineage":["https://openalex.org/I84524832"]}],"countries":["EG"],"is_corresponding":true,"raw_author_name":"A. M. A. El-Sayed","raw_affiliation_strings":["Mathematics Department, Faculty of Science, Alexandria University, Alexandria, Egypt"],"affiliations":[{"raw_affiliation_string":"Mathematics Department, Faculty of Science, Alexandria University, Alexandria, Egypt","institution_ids":["https://openalex.org/I84524832"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088123275","display_name":"Amr Elsonbaty","orcid":"https://orcid.org/0000-0001-7125-9675"},"institutions":[{"id":"https://openalex.org/I159247623","display_name":"Mansoura University","ror":"https://ror.org/01k8vtd75","country_code":"EG","type":"education","lineage":["https://openalex.org/I159247623"]}],"countries":["EG"],"is_corresponding":false,"raw_author_name":"A. Elsonbaty","raw_affiliation_strings":["Department of Mathematics and Engineering Physics, Faculty of Engineering, Mansoura University, Mansoura 35516, Egypt"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Engineering Physics, Faculty of Engineering, Mansoura University, Mansoura 35516, Egypt","institution_ids":["https://openalex.org/I159247623"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047613713","display_name":"A. A. Elsadany","orcid":"https://orcid.org/0000-0002-5010-601X"},"institutions":[{"id":"https://openalex.org/I114794399","display_name":"Suez Canal University","ror":"https://ror.org/02m82p074","country_code":"EG","type":"education","lineage":["https://openalex.org/I114794399"]}],"countries":["EG"],"is_corresponding":false,"raw_author_name":"A. A. Elsadany","raw_affiliation_strings":["Department of Basic Science, Faculty of Computers and Informatics, Ismailia 41522, Suez Canal University, Egypt"],"affiliations":[{"raw_affiliation_string":"Department of Basic Science, Faculty of Computers and Informatics, Ismailia 41522, Suez Canal University, Egypt","institution_ids":["https://openalex.org/I114794399"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5019672956","display_name":"A.E. Matouk","orcid":"https://orcid.org/0000-0001-5834-4234"},"institutions":[{"id":"https://openalex.org/I159247623","display_name":"Mansoura University","ror":"https://ror.org/01k8vtd75","country_code":"EG","type":"education","lineage":["https://openalex.org/I159247623"]}],"countries":["EG"],"is_corresponding":false,"raw_author_name":"A. E. Matouk","raw_affiliation_strings":["Mathematics Department, Faculty of Science, Mansoura University, Mansoura 35516, Egypt"],"affiliations":[{"raw_affiliation_string":"Mathematics Department, Faculty of Science, Mansoura University, Mansoura 35516, Egypt","institution_ids":["https://openalex.org/I159247623"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5100784242"],"corresponding_institution_ids":["https://openalex.org/I84524832"],"apc_list":null,"apc_paid":null,"fwci":4.4198,"has_fulltext":false,"cited_by_count":51,"citation_normalized_percentile":{"value":0.94997985,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"26","issue":"13","first_page":"1650222","last_page":"1650222"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9994999766349792,"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":0.9994999766349792,"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/T11017","display_name":"Chaos-based Image/Signal Encryption","score":0.9936000108718872,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9872999787330627,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/phase-portrait","display_name":"Phase portrait","score":0.8062757253646851},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6742212176322937},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6649851202964783},{"id":"https://openalex.org/keywords/limit-cycle","display_name":"Limit cycle","score":0.57060706615448},{"id":"https://openalex.org/keywords/lyapunov-exponent","display_name":"Lyapunov exponent","score":0.5484545826911926},{"id":"https://openalex.org/keywords/fractional-order-system","display_name":"Fractional-order system","score":0.5337207317352295},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5110212564468384},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.48136311769485474},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.47995641827583313},{"id":"https://openalex.org/keywords/hopf-bifurcation","display_name":"Hopf bifurcation","score":0.47475650906562805},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.44944268465042114},{"id":"https://openalex.org/keywords/bifurcation-diagram","display_name":"Bifurcation diagram","score":0.44823145866394043},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.44384101033210754},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.43248820304870605},{"id":"https://openalex.org/keywords/equilibrium-point","display_name":"Equilibrium point","score":0.41139766573905945},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.286565899848938},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.23677599430084229},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.18565633893013},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.18375033140182495},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.1824864149093628},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.11292624473571777},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1020975112915039},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.10172972083091736}],"concepts":[{"id":"https://openalex.org/C122283620","wikidata":"https://www.wikidata.org/wiki/Q2532943","display_name":"Phase portrait","level":4,"score":0.8062757253646851},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6742212176322937},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6649851202964783},{"id":"https://openalex.org/C93357160","wikidata":"https://www.wikidata.org/wiki/Q1545916","display_name":"Limit cycle","level":3,"score":0.57060706615448},{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.5484545826911926},{"id":"https://openalex.org/C2779728712","wikidata":"https://www.wikidata.org/wiki/Q17014617","display_name":"Fractional-order system","level":3,"score":0.5337207317352295},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5110212564468384},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.48136311769485474},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.47995641827583313},{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.47475650906562805},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.44944268465042114},{"id":"https://openalex.org/C86243350","wikidata":"https://www.wikidata.org/wiki/Q2595915","display_name":"Bifurcation diagram","level":4,"score":0.44823145866394043},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44384101033210754},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.43248820304870605},{"id":"https://openalex.org/C94766913","wikidata":"https://www.wikidata.org/wiki/Q1530271","display_name":"Equilibrium point","level":3,"score":0.41139766573905945},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.286565899848938},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.23677599430084229},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.18565633893013},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18375033140182495},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.1824864149093628},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.11292624473571777},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1020975112915039},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.10172972083091736},{"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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/s0218127416502229","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127416502229","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":61,"referenced_works":["https://openalex.org/W56786142","https://openalex.org/W194858719","https://openalex.org/W603207913","https://openalex.org/W617206983","https://openalex.org/W1632443921","https://openalex.org/W1963534727","https://openalex.org/W1963675052","https://openalex.org/W1965263041","https://openalex.org/W1966617449","https://openalex.org/W1975670568","https://openalex.org/W1984317615","https://openalex.org/W1992090309","https://openalex.org/W1998561306","https://openalex.org/W1999441336","https://openalex.org/W2000071648","https://openalex.org/W2008052025","https://openalex.org/W2011517867","https://openalex.org/W2013218122","https://openalex.org/W2025262438","https://openalex.org/W2032772553","https://openalex.org/W2034058244","https://openalex.org/W2044826366","https://openalex.org/W2051483432","https://openalex.org/W2052192147","https://openalex.org/W2055701161","https://openalex.org/W2056073865","https://openalex.org/W2056800572","https://openalex.org/W2058509690","https://openalex.org/W2063513094","https://openalex.org/W2067064980","https://openalex.org/W2068551947","https://openalex.org/W2075253754","https://openalex.org/W2088247712","https://openalex.org/W2090238903","https://openalex.org/W2091763273","https://openalex.org/W2094187171","https://openalex.org/W2094519174","https://openalex.org/W2102806043","https://openalex.org/W2110657483","https://openalex.org/W2112391778","https://openalex.org/W2135641365","https://openalex.org/W2135879504","https://openalex.org/W2141394518","https://openalex.org/W2152008523","https://openalex.org/W2152254020","https://openalex.org/W2154953502","https://openalex.org/W2155572235","https://openalex.org/W2203934738","https://openalex.org/W2219607061","https://openalex.org/W2221491749","https://openalex.org/W2303324995","https://openalex.org/W2319549932","https://openalex.org/W2344298532","https://openalex.org/W2475875455","https://openalex.org/W2482689398","https://openalex.org/W2487720785","https://openalex.org/W3102516775","https://openalex.org/W4239838448","https://openalex.org/W4246761151","https://openalex.org/W4247953052","https://openalex.org/W4253062931"],"related_works":["https://openalex.org/W2978842908","https://openalex.org/W2974193234","https://openalex.org/W2093909018","https://openalex.org/W3138933321","https://openalex.org/W2374651525","https://openalex.org/W2147537746","https://openalex.org/W2792287411","https://openalex.org/W2015939075","https://openalex.org/W1983551025","https://openalex.org/W2806452667"],"abstract_inverted_index":{"This":[0],"paper":[1],"presents":[2],"an":[3],"analytical":[4,56],"framework":[5],"to":[6,119],"investigate":[7],"the":[8,31,34,44,55,59,78,140,148],"dynamical":[9,156],"behavior":[10],"of":[11,30,33,42,61,80,91,94,155],"a":[12,62,152,170],"new":[13,149],"fractional-order":[14,69,96,142,167],"hyperchaotic":[15,97],"circuit":[16],"system.":[17,143],"A":[18,132],"sufficient":[19],"condition":[20],"for":[21,58,77],"existence,":[22],"uniqueness":[23],"and":[24,129,163],"continuous":[25],"dependence":[26],"on":[27,139],"initial":[28],"conditions":[29,57],"solution":[32],"proposed":[35,141],"system":[36,67,85,98,108,150,175],"is":[37,103,136],"derived.":[38],"The":[39,89,114,144],"local":[40],"stability":[41],"all":[43],"system\u2019s":[45],"equilibrium":[46],"points":[47],"are":[48,74,86,99,117],"discussed":[49],"using":[50,109],"fractional":[51],"Routh\u2013Hurwitz":[52],"test.":[53],"Then":[54],"existence":[60,79],"pitchfork":[63],"bifurcation":[64,82,127],"in":[65,83,106,173],"this":[66,84],"with":[68],"parameter":[70,172],"less":[71],"than":[72],"1/3":[73],"provided.":[75],"Conditions":[76],"Hopf":[81],"also":[87,104],"investigated.":[88],"dynamics":[90],"discretized":[92,107],"form":[93],"our":[95,121],"explored.":[100],"Chaos":[101],"control":[102,112],"achieved":[105],"delay":[110],"feedback":[111],"technique.":[113],"numerical":[115],"simulation":[116],"presented":[118,137],"confirm":[120],"theoretical":[122],"analysis":[123],"via":[124],"phase":[125],"portraits,":[126],"diagrams":[128],"Lyapunov":[130],"exponents.":[131],"text":[133],"encryption":[134],"algorithm":[135],"based":[138],"results":[145],"show":[146],"that":[147],"exhibits":[151],"rich":[153],"variety":[154],"behaviors":[157],"such":[158],"as":[159],"limit":[160],"cycles,":[161],"chaos":[162],"transient":[164],"phenomena":[165],"where":[166],"derivative":[168],"represents":[169],"key":[171],"determining":[174],"qualitative":[176],"behavior.":[177]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":12},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":9},{"year":2017,"cited_by_count":5}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
