Bifurcations, relaxation time, and critical exponents in a dissipative or conservative Fermi model
We investigated the time evolution for the stationary state at different bifurcations of a dissipative version of the Fermi-Ulam accelerator model. For local bifurcations, as period-doubling bifurcations, the convergence to the inactive state is made using a homogeneous and generalized function at t...
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Veröffentlicht in: | Chaos (Woodbury, N.Y.) N.Y.), 2023-02, Vol.33 (2), p.023138-023138 |
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creator | S Rando, Danilo C Martí, Arturo D Leonel, Edson |
description | We investigated the time evolution for the stationary state at different bifurcations of a dissipative version of the Fermi-Ulam accelerator model. For local bifurcations, as period-doubling bifurcations, the convergence to the inactive state is made using a homogeneous and generalized function at the bifurcation parameter. It leads to a set of three critical exponents that are universal for such bifurcation. Near bifurcation, an exponential decay describes convergence whose relaxation time is characterized by a power law. For global bifurcation, as noticed for a boundary crisis, where a chaotic transient suddenly replaces a chaotic attractor after a tiny change of control parameters, the survival probability is described by an exponential decay whose transient time is given by a power law. |
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For local bifurcations, as period-doubling bifurcations, the convergence to the inactive state is made using a homogeneous and generalized function at the bifurcation parameter. It leads to a set of three critical exponents that are universal for such bifurcation. Near bifurcation, an exponential decay describes convergence whose relaxation time is characterized by a power law. 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For global bifurcation, as noticed for a boundary crisis, where a chaotic transient suddenly replaces a chaotic attractor after a tiny change of control parameters, the survival probability is described by an exponential decay whose transient time is given by a power law.</description><subject>Bifurcations</subject><subject>Convergence</subject><subject>Decay</subject><subject>Dissipation</subject><subject>Exponents</subject><subject>Mathematical models</subject><subject>Parameters</subject><subject>Power law</subject><subject>Relaxation time</subject><issn>1054-1500</issn><issn>1089-7682</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp90F1rFTEQBuAgSj-98A9IwBst3ZrJ915qaVUoeFOvl5xkFlJ2N2uye6j_vmnPsYKgVzMDDy_DS8gbYBfAtPioLhhwKQFekCNgtm2Mtvzl465kA4qxQ3Jcyh1jlQl1QA6FtqrlwI_I5nPs1-zdEtNUzmnGwd0_HXSJI55TNwXqc1yidwPF-zlNOC2Fxok6GmIpca56izRl6msC5u3uvsY8RjqmgMMpedW7oeDr_TwhP66vbi-_Njffv3y7_HTTeAl2aVoIGhii3AjOWI_GgBVaW9dajsEqaZ2WGrQ2IhgIQfrAlRIguJPGml6ckPe73DmnnyuWpRtj8TgMbsK0lo4bC5pzrmSl7_6id2nNU_2uqhomdKtMVR92yudUSsa-m3McXf7VAesei-9Uty--2rf7xHUzYniWv5uu4GwHio_LU8P_Tfsn3qb8B3Zz6MUDm_aXwg</recordid><startdate>202302</startdate><enddate>202302</enddate><creator>S Rando, Danilo</creator><creator>C Martí, Arturo</creator><creator>D Leonel, Edson</creator><general>American Institute of Physics</general><scope>NPM</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>8FD</scope><scope>H8D</scope><scope>L7M</scope><scope>7X8</scope><orcidid>https://orcid.org/0000-0002-4053-4651</orcidid><orcidid>https://orcid.org/0000-0001-8224-3329</orcidid><orcidid>https://orcid.org/0000-0003-2023-8676</orcidid></search><sort><creationdate>202302</creationdate><title>Bifurcations, relaxation time, and critical exponents in a dissipative or conservative Fermi model</title><author>S Rando, Danilo ; C Martí, Arturo ; D Leonel, Edson</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c418t-91d610ee4b3200fe77183668a982ed8548a64616673d71dd4cd2553132a4787f3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Bifurcations</topic><topic>Convergence</topic><topic>Decay</topic><topic>Dissipation</topic><topic>Exponents</topic><topic>Mathematical models</topic><topic>Parameters</topic><topic>Power law</topic><topic>Relaxation time</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>S Rando, Danilo</creatorcontrib><creatorcontrib>C Martí, Arturo</creatorcontrib><creatorcontrib>D Leonel, Edson</creatorcontrib><collection>PubMed</collection><collection>CrossRef</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>MEDLINE - Academic</collection><jtitle>Chaos (Woodbury, N.Y.)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>S Rando, Danilo</au><au>C Martí, Arturo</au><au>D Leonel, Edson</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Bifurcations, relaxation time, and critical exponents in a dissipative or conservative Fermi model</atitle><jtitle>Chaos (Woodbury, N.Y.)</jtitle><addtitle>Chaos</addtitle><date>2023-02</date><risdate>2023</risdate><volume>33</volume><issue>2</issue><spage>023138</spage><epage>023138</epage><pages>023138-023138</pages><issn>1054-1500</issn><eissn>1089-7682</eissn><coden>CHAOEH</coden><abstract>We investigated the time evolution for the stationary state at different bifurcations of a dissipative version of the Fermi-Ulam accelerator model. 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subjects | Bifurcations Convergence Decay Dissipation Exponents Mathematical models Parameters Power law Relaxation time |
title | Bifurcations, relaxation time, and critical exponents in a dissipative or conservative Fermi model |
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