Study of the dynamic behavior of the lorentz system

Registro completo de metadados
MetadadosDescriçãoIdioma
Autor(es): dc.creatorNasri, Zakia-
Autor(es): dc.creatorBinous, Housam-
Data de aceite: dc.date.accessioned2019-08-21T19:19:59Z-
Data de disponibilização: dc.date.available2019-08-21T19:19:59Z-
Data de envio: dc.date.issued2008-12-15-
Data de envio: dc.date.issued2008-12-15-
Data de envio: dc.date.issued2008-
Data de envio: dc.date.issued2008-12-15-
Data de envio: dc.date.issued2008-11-07-
Fonte completa do material: dc.identifierhttp://objetoseducacionais2.mec.gov.br/handle/mec/8084-
Fonte: dc.identifier.urihttp://educapes.capes.gov.br/handle/capes/489522-
Descrição: dc.descriptionPartial derivatives, periodic behavior, period doubling, chaotic behavior, time-series, Lyapunov exponent-
Descrição: dc.descriptionThis Demonstration presents the dynamic behavior of the Lorentz system: dx/dt = σ (y - x) dy/dt = rx – xz – y dz/dt = xy - bz For a particular selection of model parameters σ, r and b, you can observe periodic behavior, period doubling, or chaotic behavior. The Demonstration illustrates several important concepts of nonlinear dynamics, such as the time-series plot, the phase-space diagram, the power spectrum, and the autocorrelation function plot. In addition, an estimate of the maximum Lyapunov exponent is displayed for selected model parameters-
Descrição: dc.descriptionComponente Curricular::Educação Superior::Ciências Exatas e da Terra::Matemática-
Idioma: dc.languageen-
Publicador: dc.publisherWolfram Demonstration Project-
Relação: dc.relationStudyOfTheDynamicBehaviorOfTheLorentzSystem.nbp-
Direitos: dc.rightsDemonstration freeware using Mathematica Player-
???dc.source???: dc.sourcehttp://demonstrations.wolfram.com/StudyOfTheDynamicBehaviorOfTheLorentzSystem/-
Palavras-chave: dc.subjectLyapunov exponent-
Palavras-chave: dc.subjectLorentz system-
Palavras-chave: dc.subjectDifferential Equations-
Palavras-chave: dc.subjectEducação Superior::Ciências Exatas e da Terra::Matemática::Equações Diferenciais Funcionais-
Título: dc.titleStudy of the dynamic behavior of the lorentz system-
???dc.description2???: dc.description2For σ = 16, r = 45.92 and b = 4, you can observe chaotic behavior, which is confirmed by the power spectrum diagram. The phase-space diagram is that of a strange attractor. In addition, the estimate of the maximum Lyapunov exponent is close to 1.49. A positive Lyapunov exponent is further indication of chaotic behavior. For σ = 19.8, r = 56, and b = 1, you can observe periodic behavior, which is confirmed by the power spectrum diagram. The phase-space diagram is that of a limit cycle. In addition, the estimate of the maximum Lyapunov exponent is approximately equal to zero. Thus, all Lyapunov exponents are less than zero, which is a further indication of periodic behavior-
???dc.description3???: dc.description3This demonstration needs the "MathematicaPlayer.exe" to run. Found in http://objetoseducacionais2.mec.gov.br/handle/mec/4737-
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