Dynamical estimates of chaotic systems from Poincaré recurrences
We show a function that fits well the probability density of return times between two consecutive visits of a chaotic trajectory to finite size regions in phase space. It deviates from the exponential statistics by a small power-law term, a term that represents the deterministic manifestation of the...
Gespeichert in:
| Veröffentlicht in: | Chaos (Woodbury, N.Y.) N.Y.), 2009-12, Vol.19 (4), p.043115-043115-10 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 043115-10 |
|---|---|
| container_issue | 4 |
| container_start_page | 043115 |
| container_title | Chaos (Woodbury, N.Y.) |
| container_volume | 19 |
| creator | Baptista, M. S. Maranhão, Dariel M. Sartorelli, J. C. |
| description | We show a function that fits well the probability density of return times between two consecutive visits of a chaotic trajectory to finite size regions in phase space. It deviates from the exponential statistics by a small power-law term, a term that represents the deterministic manifestation of the dynamics. We also show how one can quickly and easily estimate the Kolmogorov–Sinai entropy and the short-term correlation function by realizing observations of high probable returns. Our analyses are performed numerically in the Hénon map and experimentally in a Chua’s circuit. Finally, we discuss how our approach can be used to treat the data coming from experimental complex systems and for technological applications. |
| doi_str_mv | 10.1063/1.3263943 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_733833288</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>733833288</sourcerecordid><originalsourceid>FETCH-LOGICAL-c443t-4050467a1dd309fa98199c6a9c2053bafd6c4cf27597edb741dff0f82fbc6ff83</originalsourceid><addsrcrecordid>eNp9kMtOwzAQRS0EoqWw4AdQdgikwPiRhxcsqvKUKsEC1pYzsUVQExc7Qeon8R38GKlaygKV1czi3KuZQ8gxhQsKKb-kF5ylXAq-Q4YUchlnac52l3siYpoADMhBCG8AQBlP9smAASSSUTok4-tFo-sK9Swyoa1q3ZoQORvhq3ZthVFYhNbUIbLe1dGTqxrU_usz8gY7702DJhySPatnwRyt54i83N48T-7j6ePdw2Q8jVEI3sYCEhBppmlZcpBWy5xKiamWyCDhhbZligItyxKZmbLIBC2tBZszW2Bqbc5H5HTVO_fuveuPVXUV0MxmujGuCyrjPOec5UvybEWidyF4Y9Xc95_5haKglsIUVWthPXuybu2K2pQb8sdQD1ytgIBVq9vKNdvbNi7VxmWfP9-W_3D-N6vmpf0P_nv6N2Zrl6E</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>733833288</pqid></control><display><type>article</type><title>Dynamical estimates of chaotic systems from Poincaré recurrences</title><source>MEDLINE</source><source>AIP Journals Complete</source><source>AIP Digital Archive</source><source>Alma/SFX Local Collection</source><creator>Baptista, M. S. ; Maranhão, Dariel M. ; Sartorelli, J. C.</creator><creatorcontrib>Baptista, M. S. ; Maranhão, Dariel M. ; Sartorelli, J. C.</creatorcontrib><description>We show a function that fits well the probability density of return times between two consecutive visits of a chaotic trajectory to finite size regions in phase space. It deviates from the exponential statistics by a small power-law term, a term that represents the deterministic manifestation of the dynamics. We also show how one can quickly and easily estimate the Kolmogorov–Sinai entropy and the short-term correlation function by realizing observations of high probable returns. Our analyses are performed numerically in the Hénon map and experimentally in a Chua’s circuit. Finally, we discuss how our approach can be used to treat the data coming from experimental complex systems and for technological applications.</description><identifier>ISSN: 1054-1500</identifier><identifier>EISSN: 1089-7682</identifier><identifier>DOI: 10.1063/1.3263943</identifier><identifier>PMID: 20059211</identifier><identifier>CODEN: CHAOEH</identifier><language>eng</language><publisher>United States: American Institute of Physics</publisher><subject>Algorithms ; Computer Simulation ; Models, Statistical ; Nonlinear Dynamics</subject><ispartof>Chaos (Woodbury, N.Y.), 2009-12, Vol.19 (4), p.043115-043115-10</ispartof><rights>American Institute of Physics</rights><rights>2009 American Institute of Physics</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c443t-4050467a1dd309fa98199c6a9c2053bafd6c4cf27597edb741dff0f82fbc6ff83</citedby><cites>FETCH-LOGICAL-c443t-4050467a1dd309fa98199c6a9c2053bafd6c4cf27597edb741dff0f82fbc6ff83</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,776,780,790,1553,4498,27901,27902</link.rule.ids><backlink>$$Uhttps://www.ncbi.nlm.nih.gov/pubmed/20059211$$D View this record in MEDLINE/PubMed$$Hfree_for_read</backlink></links><search><creatorcontrib>Baptista, M. S.</creatorcontrib><creatorcontrib>Maranhão, Dariel M.</creatorcontrib><creatorcontrib>Sartorelli, J. C.</creatorcontrib><title>Dynamical estimates of chaotic systems from Poincaré recurrences</title><title>Chaos (Woodbury, N.Y.)</title><addtitle>Chaos</addtitle><description>We show a function that fits well the probability density of return times between two consecutive visits of a chaotic trajectory to finite size regions in phase space. It deviates from the exponential statistics by a small power-law term, a term that represents the deterministic manifestation of the dynamics. We also show how one can quickly and easily estimate the Kolmogorov–Sinai entropy and the short-term correlation function by realizing observations of high probable returns. Our analyses are performed numerically in the Hénon map and experimentally in a Chua’s circuit. Finally, we discuss how our approach can be used to treat the data coming from experimental complex systems and for technological applications.</description><subject>Algorithms</subject><subject>Computer Simulation</subject><subject>Models, Statistical</subject><subject>Nonlinear Dynamics</subject><issn>1054-1500</issn><issn>1089-7682</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2009</creationdate><recordtype>article</recordtype><sourceid>EIF</sourceid><recordid>eNp9kMtOwzAQRS0EoqWw4AdQdgikwPiRhxcsqvKUKsEC1pYzsUVQExc7Qeon8R38GKlaygKV1czi3KuZQ8gxhQsKKb-kF5ylXAq-Q4YUchlnac52l3siYpoADMhBCG8AQBlP9smAASSSUTok4-tFo-sK9Swyoa1q3ZoQORvhq3ZthVFYhNbUIbLe1dGTqxrU_usz8gY7702DJhySPatnwRyt54i83N48T-7j6ePdw2Q8jVEI3sYCEhBppmlZcpBWy5xKiamWyCDhhbZligItyxKZmbLIBC2tBZszW2Bqbc5H5HTVO_fuveuPVXUV0MxmujGuCyrjPOec5UvybEWidyF4Y9Xc95_5haKglsIUVWthPXuybu2K2pQb8sdQD1ytgIBVq9vKNdvbNi7VxmWfP9-W_3D-N6vmpf0P_nv6N2Zrl6E</recordid><startdate>20091201</startdate><enddate>20091201</enddate><creator>Baptista, M. S.</creator><creator>Maranhão, Dariel M.</creator><creator>Sartorelli, J. C.</creator><general>American Institute of Physics</general><scope>CGR</scope><scope>CUY</scope><scope>CVF</scope><scope>ECM</scope><scope>EIF</scope><scope>NPM</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7X8</scope></search><sort><creationdate>20091201</creationdate><title>Dynamical estimates of chaotic systems from Poincaré recurrences</title><author>Baptista, M. S. ; Maranhão, Dariel M. ; Sartorelli, J. C.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c443t-4050467a1dd309fa98199c6a9c2053bafd6c4cf27597edb741dff0f82fbc6ff83</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2009</creationdate><topic>Algorithms</topic><topic>Computer Simulation</topic><topic>Models, Statistical</topic><topic>Nonlinear Dynamics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Baptista, M. S.</creatorcontrib><creatorcontrib>Maranhão, Dariel M.</creatorcontrib><creatorcontrib>Sartorelli, J. C.</creatorcontrib><collection>Medline</collection><collection>MEDLINE</collection><collection>MEDLINE (Ovid)</collection><collection>MEDLINE</collection><collection>MEDLINE</collection><collection>PubMed</collection><collection>CrossRef</collection><collection>MEDLINE - Academic</collection><jtitle>Chaos (Woodbury, N.Y.)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Baptista, M. S.</au><au>Maranhão, Dariel M.</au><au>Sartorelli, J. C.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Dynamical estimates of chaotic systems from Poincaré recurrences</atitle><jtitle>Chaos (Woodbury, N.Y.)</jtitle><addtitle>Chaos</addtitle><date>2009-12-01</date><risdate>2009</risdate><volume>19</volume><issue>4</issue><spage>043115</spage><epage>043115-10</epage><pages>043115-043115-10</pages><issn>1054-1500</issn><eissn>1089-7682</eissn><coden>CHAOEH</coden><abstract>We show a function that fits well the probability density of return times between two consecutive visits of a chaotic trajectory to finite size regions in phase space. It deviates from the exponential statistics by a small power-law term, a term that represents the deterministic manifestation of the dynamics. We also show how one can quickly and easily estimate the Kolmogorov–Sinai entropy and the short-term correlation function by realizing observations of high probable returns. Our analyses are performed numerically in the Hénon map and experimentally in a Chua’s circuit. Finally, we discuss how our approach can be used to treat the data coming from experimental complex systems and for technological applications.</abstract><cop>United States</cop><pub>American Institute of Physics</pub><pmid>20059211</pmid><doi>10.1063/1.3263943</doi><tpages>10</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1054-1500 |
| ispartof | Chaos (Woodbury, N.Y.), 2009-12, Vol.19 (4), p.043115-043115-10 |
| issn | 1054-1500 1089-7682 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_733833288 |
| source | MEDLINE; AIP Journals Complete; AIP Digital Archive; Alma/SFX Local Collection |
| subjects | Algorithms Computer Simulation Models, Statistical Nonlinear Dynamics |
| title | Dynamical estimates of chaotic systems from Poincaré recurrences |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-03T16%3A19%3A58IST&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=Dynamical%20estimates%20of%20chaotic%20systems%20from%20Poincar%C3%A9%20recurrences&rft.jtitle=Chaos%20(Woodbury,%20N.Y.)&rft.au=Baptista,%20M.%20S.&rft.date=2009-12-01&rft.volume=19&rft.issue=4&rft.spage=043115&rft.epage=043115-10&rft.pages=043115-043115-10&rft.issn=1054-1500&rft.eissn=1089-7682&rft.coden=CHAOEH&rft_id=info:doi/10.1063/1.3263943&rft_dat=%3Cproquest_cross%3E733833288%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=733833288&rft_id=info:pmid/20059211&rfr_iscdi=true |