Effective Fokker-Planck equation for birhythmic modified van der Pol oscillator

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dc.contributor.authorYamapi, R.
dc.contributor.authorFilatrella, G.
dc.contributor.authorAziz-Alaoui, M. A.
dc.contributor.authorCerdeira, Hilda A. [UNESP]
dc.contributor.institutionUniv Douala
dc.contributor.institutionUniv Salerno
dc.contributor.institutionUniv Sannio
dc.contributor.institutionUniv Havre
dc.contributor.institutionUniversidade Estadual Paulista (Unesp)
dc.date.accessioned2013-09-30T19:03:03Z
dc.date.accessioned2014-05-20T14:14:05Z
dc.date.available2013-09-30T19:03:03Z
dc.date.available2014-05-20T14:14:05Z
dc.date.issued2012-12-01
dc.description.abstractWe present an explicit solution based on the phase-amplitude approximation of the Fokker-Planck equation associated with the Langevin equation of the birhythmic modified van der Pol system. The solution enables us to derive probability distributions analytically as well as the activation energies associated with switching between the coexisting different attractors that characterize the birhythmic system. Comparing analytical and numerical results we find good agreement when the frequencies of both attractors are equal, while the predictions of the analytic estimates deteriorate when the two frequencies depart. Under the effect of noise, the two states that characterize the birhythmic system can merge, inasmuch as the parameter plane of the birhythmic solutions is found to shrink when the noise intensity increases. The solution of the Fokker-Planck equation shows that in the birhythmic region, the two attractors are characterized by very different probabilities of finding the system in such a state. The probability becomes comparable only for a narrow range of the control parameters, thus the two limit cycles have properties in close analogy with the thermodynamic phases. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4766678]en
dc.description.affiliationUniv Douala, Fac Sci, Dept Phys, Fundamental Phys Lab, Douala, Cameroon
dc.description.affiliationUniv Salerno, Dept Phys, Salerno Unit CNSIM, I-84081 Fisciano, Italy
dc.description.affiliationUniv Sannio, Dept Sci Biol Geol & Environm Studies, I-82100 Benevento, Italy
dc.description.affiliationUniv Sannio, Salerno Unit CNSIM, I-82100 Benevento, Italy
dc.description.affiliationUniv Havre, Appl Math Lab, Le Havre, France
dc.description.affiliationUniv Estadual Paulista, Inst Fis Teor, BR-01140070 São Paulo, Brazil
dc.description.affiliationUnespUniv Estadual Paulista, Inst Fis Teor, BR-01140070 São Paulo, Brazil
dc.description.sponsorshipConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
dc.description.sponsorshipICTP (International Centre for Theoretical Physics)
dc.description.sponsorshipIdCNPq: 490265/2010-3
dc.format.extent9
dc.identifierhttp://dx.doi.org/10.1063/1.4766678
dc.identifier.citationChaos. Melville: Amer Inst Physics, v. 22, n. 4, p. 9, 2012.
dc.identifier.doi10.1063/1.4766678
dc.identifier.fileWOS000312831600014.pdf
dc.identifier.issn1054-1500
dc.identifier.urihttp://hdl.handle.net/11449/24675
dc.identifier.wosWOS:000312831600014
dc.language.isoeng
dc.publisherAmerican Institute of Physics (AIP)
dc.relation.ispartofChaos
dc.relation.ispartofjcr2.415
dc.relation.ispartofsjr0,716
dc.rights.accessRightsAcesso restrito
dc.sourceWeb of Science
dc.titleEffective Fokker-Planck equation for birhythmic modified van der Pol oscillatoren
dc.typeArtigo
dcterms.licensehttp://www.aip.org/pubservs/web_posting_guidelines.html
dcterms.rightsHolderAmer Inst Physics
unesp.campusUniversidade Estadual Paulista (Unesp), Instituto de Física Teórica (IFT), São Paulopt

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