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12 July 2009

Fractal Dimension and Analysis of Chaotic System Predictions

By: Acep Purqon
Advisor: Prof. Dr. The Houw Liong
Departemen Fisika - ITB
: Jl. Ganesa 10, Bandung
Created: 2005-01-27 , with 1 file(s).
Master Theses from JBPTITBFI / 2005-02-08 14:16:05

In 1963 Edward Lorenz successfully formulated chaotic behavior in weather. Lorenz simplified model of 2D thermal convection known as Rayleigh-Benard convection into three simultaneous ordinary differential equations called Lorenz equations. Lorenz noticed that, in his simplified mathematical model of Rayleigh-Benard convection, very small differences in the initial conditions blew up and quickly led to enormous differences in the final behavior. He reasoned that if this type of behavior could occur in such a simple dynamical system, then it may also be possible in a much more complex physical system involving convection i.e. the weather system. Almost one decade for scientists to understand the paper. Nowadays chaos becomes interesting subject to be studied in all area. The irregularities are usually measured by Lyapunov exponent, fractal dimension etc. The sentence that states the impossible prediction has challenged scientists to develop prediction methods. Many prediction methods have been developed and improved and one of it is ANFIS (Adaptive Neuro-Fuzzy Inference Systems). In this time ANFIS will be tested to analyze prediction of chaotic behavior in the Lorenz equations. The prediction results for short time are very good which coefficient of correlation for the prediction is 0.99. We also want to test how long the prediction still has good result. So we will analyze based on analysis of r-value, degree of freedom analysis, analysis of increasing amount of training data and superposition between periodic and chaotic.

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