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Title: Study of the dynamic behavior of the lorentz system
Type of Resource: Animação/simulação
Objective: For 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
Abstract: This 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
Observation: This demonstration needs the "MathematicaPlayer.exe" to run. Found in http://objetoseducacionais2.mec.gov.br/handle/mec/4737
Curriculum Component: Educação Superior::Ciências Exatas e da Terra::Matemática
Theme: Educação Superior::Ciências Exatas e da Terra::Matemática::Equações Diferenciais Funcionais
Author: Nasri, Zakia; Binous, Housam
Language: English (en)
Country: United States (us)
Publisher: Wolfram Demonstration Project
Description: Partial derivatives, periodic behavior, period doubling, chaotic behavior, time-series, Lyapunov exponent
Web Address: http://demonstrations.wolfram.com/StudyOfTheDynamicBehaviorOfTheLorentzSystem/
Date: 2008
Rightsholder: The Wolfram Demonstrations Project & Contributors
License: Demonstration freeware using Mathematica Player
Submitter: Universidade Federal de São Carlos (UFSCAR)
URI: http://objetoseducacionais2.mec.gov.br/handle/mec/8084
This Educational Object appears in the following Types of resources: Educação Superior: Ciências Exatas e da Terra: Matemática: Animações/Simulações