Extreme fractal dimension at periodicity cascades in parameter spaces
In the parameter spaces of nonlinear dynamical systems, we investigate the boundaries between periodicity and chaos and unveil the existence of fractal sets characterized by a singular fractal dimension that deviates greatly from the fractal sets in their vicinity. This extreme fractal dimension sta...
Gespeichert in:
| Veröffentlicht in: | Physical review. E 2024-09, Vol.110 (3), p.L032201, Article L032201 |
|---|---|
| Hauptverfasser: | , , , , |
| Format: | Artikel |
| Sprache: | eng |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | |
|---|---|
| container_issue | 3 |
| container_start_page | L032201 |
| container_title | Physical review. E |
| container_volume | 110 |
| creator | Abreu, Carlos E P Hermes, Joelson D V da Costa, Diogo Ricardo Medeiros, Everton S Medrano-T, Rene O |
| description | In the parameter spaces of nonlinear dynamical systems, we investigate the boundaries between periodicity and chaos and unveil the existence of fractal sets characterized by a singular fractal dimension that deviates greatly from the fractal sets in their vicinity. This extreme fractal dimension stands out from the typical value previously considered universal for these parameter boundaries. We show that such singular fractal sets dwell along parameter curves, called extreme curves, that intersect periodicity cascades at their centers of stability across all scales of parameter spaces. The results reported here are generally demonstrated for the class of one-dimensional maps with at least two control parameters. Generalizations to other classes of systems are possible. |
| doi_str_mv | 10.1103/PhysRevE.110.L032201 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_3118306087</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>3118306087</sourcerecordid><originalsourceid>FETCH-LOGICAL-c186t-8844cf4d80979c2e952f99878a76d102ef11c229c14b95f58fb12687476e86453</originalsourceid><addsrcrecordid>eNo9kFtLAzEQhYMoVmr_gUgefdk6ue0mj1LWCxQU0eclzU4wsjeTrdh_b0svTzMHzpk5fITcMJgzBuL-7WuT3vG33Kn5EgTnwM7IFZcFZABKnJ92qSZkltI3ALAcTMH4JZkII7kSUl2RsvwbI7ZIfbRutA2tQ4tdCn1H7UgHjKGvgwvjhjqbnK0x0dDRwUbb4oiRpsE6TNfkwtsm4ewwp-TzsfxYPGfL16eXxcMyc0znY6a1lM7LWm97GMfRKO6N0YW2RV4z4OgZc5wbx-TKKK-0XzGe60IWOepcKjEld_u7Q-x_1pjGqg3JYdPYDvt1qgRjWkAOutha5d7qYp9SRF8NMbQ2bioG1Y5hdWS4U9WB4TZ2e_iwXrVYn0JHYuIfX0BtcA</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>3118306087</pqid></control><display><type>article</type><title>Extreme fractal dimension at periodicity cascades in parameter spaces</title><source>American Physical Society Journals</source><creator>Abreu, Carlos E P ; Hermes, Joelson D V ; da Costa, Diogo Ricardo ; Medeiros, Everton S ; Medrano-T, Rene O</creator><creatorcontrib>Abreu, Carlos E P ; Hermes, Joelson D V ; da Costa, Diogo Ricardo ; Medeiros, Everton S ; Medrano-T, Rene O</creatorcontrib><description>In the parameter spaces of nonlinear dynamical systems, we investigate the boundaries between periodicity and chaos and unveil the existence of fractal sets characterized by a singular fractal dimension that deviates greatly from the fractal sets in their vicinity. This extreme fractal dimension stands out from the typical value previously considered universal for these parameter boundaries. We show that such singular fractal sets dwell along parameter curves, called extreme curves, that intersect periodicity cascades at their centers of stability across all scales of parameter spaces. The results reported here are generally demonstrated for the class of one-dimensional maps with at least two control parameters. Generalizations to other classes of systems are possible.</description><identifier>ISSN: 2470-0045</identifier><identifier>ISSN: 2470-0053</identifier><identifier>EISSN: 2470-0053</identifier><identifier>DOI: 10.1103/PhysRevE.110.L032201</identifier><identifier>PMID: 39425345</identifier><language>eng</language><publisher>United States</publisher><ispartof>Physical review. E, 2024-09, Vol.110 (3), p.L032201, Article L032201</ispartof><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c186t-8844cf4d80979c2e952f99878a76d102ef11c229c14b95f58fb12687476e86453</cites><orcidid>0000-0002-9600-6305 ; 0000-0003-0866-2466 ; 0000-0002-2869-0184 ; 0000-0001-8531-6327</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,776,780,2863,2864,27901,27902</link.rule.ids><backlink>$$Uhttps://www.ncbi.nlm.nih.gov/pubmed/39425345$$D View this record in MEDLINE/PubMed$$Hfree_for_read</backlink></links><search><creatorcontrib>Abreu, Carlos E P</creatorcontrib><creatorcontrib>Hermes, Joelson D V</creatorcontrib><creatorcontrib>da Costa, Diogo Ricardo</creatorcontrib><creatorcontrib>Medeiros, Everton S</creatorcontrib><creatorcontrib>Medrano-T, Rene O</creatorcontrib><title>Extreme fractal dimension at periodicity cascades in parameter spaces</title><title>Physical review. E</title><addtitle>Phys Rev E</addtitle><description>In the parameter spaces of nonlinear dynamical systems, we investigate the boundaries between periodicity and chaos and unveil the existence of fractal sets characterized by a singular fractal dimension that deviates greatly from the fractal sets in their vicinity. This extreme fractal dimension stands out from the typical value previously considered universal for these parameter boundaries. We show that such singular fractal sets dwell along parameter curves, called extreme curves, that intersect periodicity cascades at their centers of stability across all scales of parameter spaces. The results reported here are generally demonstrated for the class of one-dimensional maps with at least two control parameters. Generalizations to other classes of systems are possible.</description><issn>2470-0045</issn><issn>2470-0053</issn><issn>2470-0053</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><recordid>eNo9kFtLAzEQhYMoVmr_gUgefdk6ue0mj1LWCxQU0eclzU4wsjeTrdh_b0svTzMHzpk5fITcMJgzBuL-7WuT3vG33Kn5EgTnwM7IFZcFZABKnJ92qSZkltI3ALAcTMH4JZkII7kSUl2RsvwbI7ZIfbRutA2tQ4tdCn1H7UgHjKGvgwvjhjqbnK0x0dDRwUbb4oiRpsE6TNfkwtsm4ewwp-TzsfxYPGfL16eXxcMyc0znY6a1lM7LWm97GMfRKO6N0YW2RV4z4OgZc5wbx-TKKK-0XzGe60IWOepcKjEld_u7Q-x_1pjGqg3JYdPYDvt1qgRjWkAOutha5d7qYp9SRF8NMbQ2bioG1Y5hdWS4U9WB4TZ2e_iwXrVYn0JHYuIfX0BtcA</recordid><startdate>202409</startdate><enddate>202409</enddate><creator>Abreu, Carlos E P</creator><creator>Hermes, Joelson D V</creator><creator>da Costa, Diogo Ricardo</creator><creator>Medeiros, Everton S</creator><creator>Medrano-T, Rene O</creator><scope>NPM</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7X8</scope><orcidid>https://orcid.org/0000-0002-9600-6305</orcidid><orcidid>https://orcid.org/0000-0003-0866-2466</orcidid><orcidid>https://orcid.org/0000-0002-2869-0184</orcidid><orcidid>https://orcid.org/0000-0001-8531-6327</orcidid></search><sort><creationdate>202409</creationdate><title>Extreme fractal dimension at periodicity cascades in parameter spaces</title><author>Abreu, Carlos E P ; Hermes, Joelson D V ; da Costa, Diogo Ricardo ; Medeiros, Everton S ; Medrano-T, Rene O</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c186t-8844cf4d80979c2e952f99878a76d102ef11c229c14b95f58fb12687476e86453</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Abreu, Carlos E P</creatorcontrib><creatorcontrib>Hermes, Joelson D V</creatorcontrib><creatorcontrib>da Costa, Diogo Ricardo</creatorcontrib><creatorcontrib>Medeiros, Everton S</creatorcontrib><creatorcontrib>Medrano-T, Rene O</creatorcontrib><collection>PubMed</collection><collection>CrossRef</collection><collection>MEDLINE - Academic</collection><jtitle>Physical review. E</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Abreu, Carlos E P</au><au>Hermes, Joelson D V</au><au>da Costa, Diogo Ricardo</au><au>Medeiros, Everton S</au><au>Medrano-T, Rene O</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Extreme fractal dimension at periodicity cascades in parameter spaces</atitle><jtitle>Physical review. E</jtitle><addtitle>Phys Rev E</addtitle><date>2024-09</date><risdate>2024</risdate><volume>110</volume><issue>3</issue><spage>L032201</spage><pages>L032201-</pages><artnum>L032201</artnum><issn>2470-0045</issn><issn>2470-0053</issn><eissn>2470-0053</eissn><abstract>In the parameter spaces of nonlinear dynamical systems, we investigate the boundaries between periodicity and chaos and unveil the existence of fractal sets characterized by a singular fractal dimension that deviates greatly from the fractal sets in their vicinity. This extreme fractal dimension stands out from the typical value previously considered universal for these parameter boundaries. We show that such singular fractal sets dwell along parameter curves, called extreme curves, that intersect periodicity cascades at their centers of stability across all scales of parameter spaces. The results reported here are generally demonstrated for the class of one-dimensional maps with at least two control parameters. Generalizations to other classes of systems are possible.</abstract><cop>United States</cop><pmid>39425345</pmid><doi>10.1103/PhysRevE.110.L032201</doi><orcidid>https://orcid.org/0000-0002-9600-6305</orcidid><orcidid>https://orcid.org/0000-0003-0866-2466</orcidid><orcidid>https://orcid.org/0000-0002-2869-0184</orcidid><orcidid>https://orcid.org/0000-0001-8531-6327</orcidid></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 2470-0045 |
| ispartof | Physical review. E, 2024-09, Vol.110 (3), p.L032201, Article L032201 |
| issn | 2470-0045 2470-0053 2470-0053 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_3118306087 |
| source | American Physical Society Journals |
| title | Extreme fractal dimension at periodicity cascades in parameter spaces |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-31T18%3A23%3A35IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Extreme%20fractal%20dimension%20at%20periodicity%20cascades%20in%20parameter%20spaces&rft.jtitle=Physical%20review.%20E&rft.au=Abreu,%20Carlos%20E%20P&rft.date=2024-09&rft.volume=110&rft.issue=3&rft.spage=L032201&rft.pages=L032201-&rft.artnum=L032201&rft.issn=2470-0045&rft.eissn=2470-0053&rft_id=info:doi/10.1103/PhysRevE.110.L032201&rft_dat=%3Cproquest_cross%3E3118306087%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=3118306087&rft_id=info:pmid/39425345&rfr_iscdi=true |