LYAPUNOV EXPONENT AND DIMENSIONS OF THE ATTRACTOR FOR TWO DIMENSIONAL NEURAL MODEL
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Abstract
In this paper a two dimensional non linear neural network model is considered and it is shown that chaotic attractor exists beyond accumulation point. To confirm the existence of chaotic attractor, Lyapunov exponent method is used. Further various fractal dimensions like Correlation dimension, Box-counting and Information dimension of the chaotic attractor were found to assess the geometry of the fractal set.
Keywords: Lyapunov  Exponent, Strange attractor, fractal dimension, Correlation dimension, Box-counting and Information dimension.
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References
Crownover,R.M., “Introduction to Fractals and Chaosâ€, Jones and Bartlett,Sudbury,MA,1995.
] Dutta, T.K, Jain.A.K and Bhattacharjee.D., “Determination of various fractal dimensions in one dimensional models†IJST,Vol-2,Issue-3,2013,ISSN 2249-9954.
Dutta, T.K, Jain.A.K and Bhattacharjee.D., “Period Doubling Scenario Exhibit on Artificial Neural Network Model†JGRMA,Vol-1,Issue-6,2013,ISSN 2320-5822.
Dutta, T.K, and Bhattacharjee.D, Bifurcation, “Lyapunov Exponent and fractal Dimensions in a Non-linear Map†[2010 AMS Classification: 37G15, 37G35, 37C45].
Falconer, K., “Fractal Geometry : Mathematical Foundations and Applicationsâ€, Wiley, New York,2003.
Grassberger.P., “Generalised Dimension of the Strange Attractors†, Physics Letters,Vol-97A,No-6,1983.
Grassberger, P.,Procaccia,I., “Characterization of strange Attractorsâ€, Physical Review Letters,Vol-50,No-5,1983.
Hilborn, R. C., “Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineersâ€. , Oxford University Press, 1994.
Moon.F.C., “Chaos and fractal dynamics†,1992
Ott.E., “Strange attractors and chaotic motions of dynamical systemsâ€, Rev.Mod .Phys.,Vol- 53,No.4,Part 1 ,Oct 1981.
Sandri M., “Numerical Calculation of Lyapunov Exponent †The Mathematica Journal ,Miller freeman Publications,1996, Vol 6,Issue 3.
Theiler.J., “Estimating Fractal Dimensionâ€, J.Opt.Soc.Am.A pp.1050-1073,Vol-7,No.6, June 1990.