Dynamical properties of a particle in a wave packet: Scaling invariance and boundary crisis

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dc.contributor.authorOliveira, Diego F. M.
dc.contributor.authorRobnik, Marko
dc.contributor.authorLeonel, Edson Denis [UNESP]
dc.contributor.institutionUniv Maribor
dc.contributor.institutionUniversidade Estadual Paulista (Unesp)
dc.date.accessioned2013-09-30T18:50:26Z
dc.date.accessioned2014-05-20T14:16:18Z
dc.date.available2013-09-30T18:50:26Z
dc.date.available2014-05-20T14:16:18Z
dc.date.issued2011-10-01
dc.description.abstractSome dynamical properties present in a problem concerning the acceleration of particles in a wave packet are studied. The dynamics of the model is described in terms of a two-dimensional area preserving map. We show that the phase space is mixed in the sense that there are regular and chaotic regions coexisting. We use a connection with the standard map in order to find the position of the first invariant spanning curve which borders the chaotic sea. We find that the position of the first invariant spanning curve increases as a power of the control parameter with the exponent 2/3. The standard deviation of the kinetic energy of an ensemble of initial conditions obeys a power law as a function of time, and saturates after some crossover. Scaling formalism is used in order to characterise the chaotic region close to the transition from integrability to nonintegrability and a relationship between the power law exponents is derived. The formalism can be applied in many different systems with mixed phase space. Then, dissipation is introduced into the model and therefore the property of area preservation is broken, and consequently attractors are observed. We show that after a small change of the dissipation, the chaotic attractor as well as its basin of attraction are destroyed, thus leading the system to experience a boundary crisis. The transient after the crisis follows a power law with exponent -2. (C) 2011 Elsevier Ltd. All rights reserved.en
dc.description.affiliationUniv Maribor, CAMTP, SI-2000 Maribor, Slovenia
dc.description.affiliationUniv Estadual Paulista, UNESP, Dept Estat Matemat Aplicada & Comp, BR-13506900 Rio Claro, SP, Brazil
dc.description.affiliationUnespUniv Estadual Paulista, UNESP, Dept Estat Matemat Aplicada & Comp, BR-13506900 Rio Claro, SP, Brazil
dc.description.sponsorshipAd futura Foundation
dc.description.sponsorshipSlovenian Research Agency (ARRS)
dc.format.extent883-890
dc.identifierhttp://dx.doi.org/10.1016/j.chaos.2011.07.001
dc.identifier.citationChaos Solitons & Fractals. Oxford: Pergamon-Elsevier B.V. Ltd, v. 44, n. 10, p. 883-890, 2011.
dc.identifier.doi10.1016/j.chaos.2011.07.001
dc.identifier.issn0960-0779
dc.identifier.lattes6130644232718610
dc.identifier.orcid0000-0001-8224-3329
dc.identifier.urihttp://hdl.handle.net/11449/24906
dc.identifier.wosWOS:000296409900013
dc.language.isoeng
dc.publisherPergamon-Elsevier B.V. Ltd
dc.relation.ispartofChaos Solitons & Fractals
dc.relation.ispartofjcr2.213
dc.relation.ispartofsjr0,678
dc.rights.accessRightsAcesso restrito
dc.sourceWeb of Science
dc.titleDynamical properties of a particle in a wave packet: Scaling invariance and boundary crisisen
dc.typeArtigo
dcterms.licensehttp://www.elsevier.com/about/open-access/open-access-policies/article-posting-policy
dcterms.rightsHolderPergamon-Elsevier B.V. Ltd
unesp.author.lattes6130644232718610[3]
unesp.author.orcid0000-0001-8224-3329[3]
unesp.campusUniversidade Estadual Paulista (Unesp), Instituto de Geociências e Ciências Exatas, Rio Claropt

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Artigos - Estatistica, Matemática Aplicada e Computação - IGCE