Universal shape law of stochastic supercritical bifurcations: Theory and experiments

Universal shape law of stochastic supercritical bifurcations: Theory and experiments

A universal law for the supercritical bifurcation shape of transverse one-dimensional (1D) systems in presence of additive noise is given. The stochastic Langevin equation of such systems is solved by using a Fokker-Planck equation leading to the expression for the most probable amplitude of the cri...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:arXiv.org 2007-02
Hauptverfasser: Agez, Gonzague, Clerc, Marcel G, Louvergneaux, Eric
Format: Artikel
Sprache:eng
Schlagworte:
Bifurcation theory
Fokker-Planck equation
Optical feedback
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page
container_issue
container_start_page
container_title arXiv.org
container_volume
creator Agez, Gonzague
Clerc, Marcel G
Louvergneaux, Eric
description A universal law for the supercritical bifurcation shape of transverse one-dimensional (1D) systems in presence of additive noise is given. The stochastic Langevin equation of such systems is solved by using a Fokker-Planck equation leading to the expression for the most probable amplitude of the critical mode. From this universal expression, the shape of the bifurcation, its location and its evolution with the noise level are completely defined. Experimental results obtained for a 1D transverse Kerr-like slice subjected to optical feedback are in excellent agreement.
doi_str_mv 10.48550/arxiv.0702057
format Article
fullrecord <record><control><sourceid>proquest</sourceid><recordid>TN_cdi_proquest_journals_2090088768</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2090088768</sourcerecordid><originalsourceid>FETCH-proquest_journals_20900887683</originalsourceid><addsrcrecordid>eNqNyrEOgjAUheHGxESjrM5NnMFLsVJdjcYHwJnUWkINtthbEN9eBh_A6fzJ-QhZpZBsBeewkX4wfQI5MOD5hMxZlqWx2DI2IxHiAwDYLmecZ3NSXK3ptUfZUKxlq2kj39RVFINTtcRgFMWu1V55M_aobqbqvJLBOIsHWtTa-Q-V9k71MDLz1Dbgkkwr2aCOfrsg6_OpOF7i1rtXpzGUD9d5O14lgz2AEPlOZP-pL8wURyc</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2090088768</pqid></control><display><type>article</type><title>Universal shape law of stochastic supercritical bifurcations: Theory and experiments</title><source>Free E- Journals</source><creator>Agez, Gonzague ; Clerc, Marcel G ; Louvergneaux, Eric</creator><creatorcontrib>Agez, Gonzague ; Clerc, Marcel G ; Louvergneaux, Eric</creatorcontrib><description>A universal law for the supercritical bifurcation shape of transverse one-dimensional (1D) systems in presence of additive noise is given. The stochastic Langevin equation of such systems is solved by using a Fokker-Planck equation leading to the expression for the most probable amplitude of the critical mode. From this universal expression, the shape of the bifurcation, its location and its evolution with the noise level are completely defined. Experimental results obtained for a 1D transverse Kerr-like slice subjected to optical feedback are in excellent agreement.</description><identifier>EISSN: 2331-8422</identifier><identifier>DOI: 10.48550/arxiv.0702057</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Bifurcation theory ; Fokker-Planck equation ; Optical feedback</subject><ispartof>arXiv.org, 2007-02</ispartof><rights>Notwithstanding the ProQuest Terms and conditions, you may use this content in accordance with the associated terms available at http://arxiv.org/abs/nlin/0702057.</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>780,784,27924</link.rule.ids></links><search><creatorcontrib>Agez, Gonzague</creatorcontrib><creatorcontrib>Clerc, Marcel G</creatorcontrib><creatorcontrib>Louvergneaux, Eric</creatorcontrib><title>Universal shape law of stochastic supercritical bifurcations: Theory and experiments</title><title>arXiv.org</title><description>A universal law for the supercritical bifurcation shape of transverse one-dimensional (1D) systems in presence of additive noise is given. The stochastic Langevin equation of such systems is solved by using a Fokker-Planck equation leading to the expression for the most probable amplitude of the critical mode. From this universal expression, the shape of the bifurcation, its location and its evolution with the noise level are completely defined. Experimental results obtained for a 1D transverse Kerr-like slice subjected to optical feedback are in excellent agreement.</description><subject>Bifurcation theory</subject><subject>Fokker-Planck equation</subject><subject>Optical feedback</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2007</creationdate><recordtype>article</recordtype><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><recordid>eNqNyrEOgjAUheHGxESjrM5NnMFLsVJdjcYHwJnUWkINtthbEN9eBh_A6fzJ-QhZpZBsBeewkX4wfQI5MOD5hMxZlqWx2DI2IxHiAwDYLmecZ3NSXK3ptUfZUKxlq2kj39RVFINTtcRgFMWu1V55M_aobqbqvJLBOIsHWtTa-Q-V9k71MDLz1Dbgkkwr2aCOfrsg6_OpOF7i1rtXpzGUD9d5O14lgz2AEPlOZP-pL8wURyc</recordid><startdate>20070228</startdate><enddate>20070228</enddate><creator>Agez, Gonzague</creator><creator>Clerc, Marcel G</creator><creator>Louvergneaux, Eric</creator><general>Cornell University Library, arXiv.org</general><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope></search><sort><creationdate>20070228</creationdate><title>Universal shape law of stochastic supercritical bifurcations: Theory and experiments</title><author>Agez, Gonzague ; Clerc, Marcel G ; Louvergneaux, Eric</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-proquest_journals_20900887683</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2007</creationdate><topic>Bifurcation theory</topic><topic>Fokker-Planck equation</topic><topic>Optical feedback</topic><toplevel>online_resources</toplevel><creatorcontrib>Agez, Gonzague</creatorcontrib><creatorcontrib>Clerc, Marcel G</creatorcontrib><creatorcontrib>Louvergneaux, Eric</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science &amp; Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Publicly Available Content Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Agez, Gonzague</au><au>Clerc, Marcel G</au><au>Louvergneaux, Eric</au><format>book</format><genre>document</genre><ristype>GEN</ristype><atitle>Universal shape law of stochastic supercritical bifurcations: Theory and experiments</atitle><jtitle>arXiv.org</jtitle><date>2007-02-28</date><risdate>2007</risdate><eissn>2331-8422</eissn><abstract>A universal law for the supercritical bifurcation shape of transverse one-dimensional (1D) systems in presence of additive noise is given. The stochastic Langevin equation of such systems is solved by using a Fokker-Planck equation leading to the expression for the most probable amplitude of the critical mode. From this universal expression, the shape of the bifurcation, its location and its evolution with the noise level are completely defined. Experimental results obtained for a 1D transverse Kerr-like slice subjected to optical feedback are in excellent agreement.</abstract><cop>Ithaca</cop><pub>Cornell University Library, arXiv.org</pub><doi>10.48550/arxiv.0702057</doi><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier EISSN: 2331-8422
ispartof arXiv.org, 2007-02
issn 2331-8422
language eng
recordid cdi_proquest_journals_2090088768
source Free E- Journals
subjects Bifurcation theory
Fokker-Planck equation
Optical feedback
title Universal shape law of stochastic supercritical bifurcations: Theory and experiments
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-12T22%3A38%3A53IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest&rft_val_fmt=info:ofi/fmt:kev:mtx:book&rft.genre=document&rft.atitle=Universal%20shape%20law%20of%20stochastic%20supercritical%20bifurcations:%20Theory%20and%20experiments&rft.jtitle=arXiv.org&rft.au=Agez,%20Gonzague&rft.date=2007-02-28&rft.eissn=2331-8422&rft_id=info:doi/10.48550/arxiv.0702057&rft_dat=%3Cproquest%3E2090088768%3C/proquest%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2090088768&rft_id=info:pmid/&rfr_iscdi=true