{"id":"https://openalex.org/W4403939500","doi":"https://doi.org/10.3390/sym16111447","title":"Asymmetry and Symmetry in New Three-Dimensional Chaotic Map with Commensurate and Incommensurate Fractional Orders","display_name":"Asymmetry and Symmetry in New Three-Dimensional Chaotic Map with Commensurate and Incommensurate Fractional Orders","publication_year":2024,"publication_date":"2024-10-31","ids":{"openalex":"https://openalex.org/W4403939500","doi":"https://doi.org/10.3390/sym16111447"},"language":"en","primary_location":{"id":"doi:10.3390/sym16111447","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16111447","pdf_url":"https://www.mdpi.com/2073-8994/16/11/1447/pdf?version=1730451726","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/16/11/1447/pdf?version=1730451726","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001446002","display_name":"H. Al-Ta\u2019ani","orcid":"https://orcid.org/0000-0001-7644-9937"},"institutions":[{"id":"https://openalex.org/I230091363","display_name":"German Jordanian University","ror":"https://ror.org/02jgpyd84","country_code":"JO","type":"education","lineage":["https://openalex.org/I230091363"]}],"countries":["JO"],"is_corresponding":false,"raw_author_name":"Hussein Al-Taani","raw_affiliation_strings":["School of Electrical Engineering and Information Technology, German Jordanian University, Amman 11180, Jordan"],"affiliations":[{"raw_affiliation_string":"School of Electrical Engineering and Information Technology, German Jordanian University, Amman 11180, Jordan","institution_ids":["https://openalex.org/I230091363"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5113276599","display_name":"Ma\u2019mon Abu Hammad","orcid":null},"institutions":[{"id":"https://openalex.org/I145019703","display_name":"Al-Zaytoonah University of Jordan","ror":"https://ror.org/04a5b0p13","country_code":"JO","type":"education","lineage":["https://openalex.org/I145019703"]}],"countries":["JO"],"is_corresponding":false,"raw_author_name":"Ma\u2019mon Abu Hammad","raw_affiliation_strings":["Department of Mathematics, Al-Zaytoonah University of Jordan, Amman 11733, Jordan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Al-Zaytoonah University of Jordan, Amman 11733, Jordan","institution_ids":["https://openalex.org/I145019703"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049312709","display_name":"Mohammad Abudayah","orcid":"https://orcid.org/0000-0001-9671-4961"},"institutions":[{"id":"https://openalex.org/I230091363","display_name":"German Jordanian University","ror":"https://ror.org/02jgpyd84","country_code":"JO","type":"education","lineage":["https://openalex.org/I230091363"]}],"countries":["JO"],"is_corresponding":false,"raw_author_name":"Mohammad Abudayah","raw_affiliation_strings":["School of Electrical Engineering and Information Technology, German Jordanian University, Amman 11180, Jordan"],"affiliations":[{"raw_affiliation_string":"School of Electrical Engineering and Information Technology, German Jordanian University, Amman 11180, Jordan","institution_ids":["https://openalex.org/I230091363"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5099847357","display_name":"Louiza Diabi","orcid":null},"institutions":[{"id":"https://openalex.org/I3132180716","display_name":"Larbi Ben M'hidi University of Oum El Bouaghi","ror":"https://ror.org/0034tbg85","country_code":"DZ","type":"education","lineage":["https://openalex.org/I3132180716"]}],"countries":["DZ"],"is_corresponding":true,"raw_author_name":"Louiza Diabi","raw_affiliation_strings":["Laboratory of Dynamical Systems and Control, University of Larbi Ben M\u2019hidi, Oum El Bouaghi 04000, Algeria","Laboratory of Dynamical Systems and Control, University of Larbi Ben M'hidi, Oum El Bouaghi 04000, Algeria"],"affiliations":[{"raw_affiliation_string":"Laboratory of Dynamical Systems and Control, University of Larbi Ben M\u2019hidi, Oum El Bouaghi 04000, Algeria","institution_ids":["https://openalex.org/I3132180716"]},{"raw_affiliation_string":"Laboratory of Dynamical Systems and Control, University of Larbi Ben M'hidi, Oum El Bouaghi 04000, Algeria","institution_ids":["https://openalex.org/I3132180716"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027644473","display_name":"Adel Ouannas","orcid":"https://orcid.org/0000-0001-9611-2047"},"institutions":[{"id":"https://openalex.org/I3132180716","display_name":"Larbi Ben M'hidi University of Oum El Bouaghi","ror":"https://ror.org/0034tbg85","country_code":"DZ","type":"education","lineage":["https://openalex.org/I3132180716"]}],"countries":["DZ"],"is_corresponding":false,"raw_author_name":"Adel Ouannas","raw_affiliation_strings":["Department of Mathematics and Computer Sciences, University of Larbi Ben M\u2019hidi, Oum El Bouaghi 04000, Algeria","Department of Mathematics and Computer Sciences, University of Larbi Ben M'hidi, Oum El Bouaghi 04000, Algeria"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Sciences, University of Larbi Ben M\u2019hidi, Oum El Bouaghi 04000, Algeria","institution_ids":["https://openalex.org/I3132180716"]},{"raw_affiliation_string":"Department of Mathematics and Computer Sciences, University of Larbi Ben M'hidi, Oum El Bouaghi 04000, Algeria","institution_ids":["https://openalex.org/I3132180716"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5099847357"],"corresponding_institution_ids":["https://openalex.org/I3132180716"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":2.0262,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.86949037,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"16","issue":"11","first_page":"1447","last_page":"1447"},"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/T12946","display_name":"Fractal and DNA sequence analysis","score":0.9761999845504761,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9710000157356262,"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":0.8662664890289307},{"id":"https://openalex.org/keywords/lyapunov-exponent","display_name":"Lyapunov exponent","score":0.7887712121009827},{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.7417482137680054},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.7364287376403809},{"id":"https://openalex.org/keywords/asymmetry","display_name":"Asymmetry","score":0.7004313468933105},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.5654407739639282},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5196634531021118},{"id":"https://openalex.org/keywords/logistic-map","display_name":"Logistic map","score":0.5143450498580933},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.5099080801010132},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.4632011950016022},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.4587230384349823},{"id":"https://openalex.org/keywords/approximate-entropy","display_name":"Approximate entropy","score":0.45811763405799866},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4114406108856201},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.33789148926734924},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.3350920081138611},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.30177080631256104},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.29910022020339966},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09358304738998413},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08051270246505737},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07393145561218262}],"concepts":[{"id":"https://openalex.org/C122283620","wikidata":"https://www.wikidata.org/wiki/Q2532943","display_name":"Phase portrait","level":4,"score":0.8662664890289307},{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.7887712121009827},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.7417482137680054},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.7364287376403809},{"id":"https://openalex.org/C38976095","wikidata":"https://www.wikidata.org/wiki/Q752641","display_name":"Asymmetry","level":2,"score":0.7004313468933105},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5654407739639282},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5196634531021118},{"id":"https://openalex.org/C205330730","wikidata":"https://www.wikidata.org/wiki/Q587182","display_name":"Logistic map","level":3,"score":0.5143450498580933},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.5099080801010132},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.4632011950016022},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.4587230384349823},{"id":"https://openalex.org/C86859247","wikidata":"https://www.wikidata.org/wiki/Q4781760","display_name":"Approximate entropy","level":3,"score":0.45811763405799866},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4114406108856201},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.33789148926734924},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.3350920081138611},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.30177080631256104},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29910022020339966},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09358304738998413},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08051270246505737},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07393145561218262}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/sym16111447","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16111447","pdf_url":"https://www.mdpi.com/2073-8994/16/11/1447/pdf?version=1730451726","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:7fdf761a528c4bb3995a934f485fab71","is_oa":true,"landing_page_url":"https://doaj.org/article/7fdf761a528c4bb3995a934f485fab71","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 16, Iss 11, p 1447 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/sym16111447","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16111447","pdf_url":"https://www.mdpi.com/2073-8994/16/11/1447/pdf?version=1730451726","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4403939500.pdf","grobid_xml":"https://content.openalex.org/works/W4403939500.grobid-xml"},"referenced_works_count":44,"referenced_works":["https://openalex.org/W1862394037","https://openalex.org/W2031064583","https://openalex.org/W2063889362","https://openalex.org/W2088303893","https://openalex.org/W2095360730","https://openalex.org/W2506955103","https://openalex.org/W2567237076","https://openalex.org/W2593904818","https://openalex.org/W2606659012","https://openalex.org/W2754371488","https://openalex.org/W2790741054","https://openalex.org/W2949131092","https://openalex.org/W2971637334","https://openalex.org/W2977209716","https://openalex.org/W2982509241","https://openalex.org/W3012197737","https://openalex.org/W3016750353","https://openalex.org/W3017356998","https://openalex.org/W3108361546","https://openalex.org/W3139528947","https://openalex.org/W3152600402","https://openalex.org/W3170201260","https://openalex.org/W3183095410","https://openalex.org/W4226177137","https://openalex.org/W4281683510","https://openalex.org/W4308558951","https://openalex.org/W4310118226","https://openalex.org/W4313254857","https://openalex.org/W4313472537","https://openalex.org/W4320727327","https://openalex.org/W4353069602","https://openalex.org/W4380877250","https://openalex.org/W4386074059","https://openalex.org/W4387667593","https://openalex.org/W4392192445","https://openalex.org/W4392747828","https://openalex.org/W4400280166","https://openalex.org/W4401596235","https://openalex.org/W4401756577","https://openalex.org/W4408974088","https://openalex.org/W6724582019","https://openalex.org/W6736543396","https://openalex.org/W6744281372","https://openalex.org/W6775995506"],"related_works":["https://openalex.org/W1083439616","https://openalex.org/W2023046846","https://openalex.org/W2347531085","https://openalex.org/W1628429654","https://openalex.org/W3111883714","https://openalex.org/W2542960427","https://openalex.org/W2951182675","https://openalex.org/W3111547351","https://openalex.org/W2032407639","https://openalex.org/W2368906896"],"abstract_inverted_index":{"According":[0],"to":[1,10],"recent":[2],"research,":[3],"discrete-time":[4],"fractional-order":[5],"models":[6],"have":[7],"greater":[8],"potential":[9],"investigate":[11],"behaviors,":[12,105],"and":[13,42,58,67,80,88,111],"chaotic":[14,32,70,95],"maps":[15],"with":[16],"fractional":[17,31,94],"derivative":[18,90],"values":[19,91],"exhibit":[20,100],"rich":[21],"dynamics.":[22,49],"This":[23],"manuscript":[24],"studies":[25],"the":[26,38,51,65,69,73,76,86,93,114,129,133],"dynamics":[27],"of":[28,103],"a":[29,101,119],"new":[30,115],"map-based":[33,96],"three":[34,97],"functions.":[35],"We":[36],"analyze":[37],"behaviors":[39],"in":[40,72],"commensurate":[41,87],"incommensurate":[43,89],"orders,":[44],"revealing":[45],"their":[46],"impact":[47],"on":[48],"Through":[50],"maximum":[52],"Lyapunov":[53],"exponent":[54],"(LEmax),":[55],"phase":[56],"portraits,":[57],"bifurcation":[59],"charts.":[60],"In":[61],"addition,":[62],"we":[63],"assess":[64],"complexity":[66],"confirm":[68],"features":[71],"map":[74],"using":[75,132],"approximation":[77],"entropy":[78],"ApEn":[79],"C0":[81],"complexity.":[82],"Studies":[83],"show":[84],"that":[85],"influence":[92],"functions,":[98],"which":[99],"variety":[102],"dynamical":[104],"such":[106],"as":[107],"hidden":[108],"attractors,":[109],"asymmetry,":[110],"symmetry.":[112],"Moreover,":[113],"system\u2019s":[116],"stabilizing":[117],"employing":[118],"3D":[120],"nonlinear":[121],"controller":[122],"is":[123],"introduced.":[124],"Finally,":[125],"our":[126],"study":[127],"validates":[128],"research":[130],"results":[131],"simulation":[134],"MATLAB":[135],"R2024a.":[136]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":6}],"updated_date":"2026-03-13T14:20:09.374765","created_date":"2025-10-10T00:00:00"}