LYAPUNOV EXPONENT AND DIMENSIONS OF THE ATTRACTOR FOR TWO DIMENSIONAL NEURAL MODEL

T.K. Dutta

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.


Full Text:

PDF

References


Crownover,R.M., “Introduction to Fractals and Chaos”, 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 Applications”, 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 Attractors”, Physical Review Letters,Vol-50,No-5,1983.

Hilborn, R. C., “Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers”. , Oxford University Press, 1994.

Moon.F.C., “Chaos and fractal dynamics” ,1992

Ott.E., “Strange attractors and chaotic motions of dynamical systems”, 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 Dimension”, J.Opt.Soc.Am.A pp.1050-1073,Vol-7,No.6, June 1990.


Refbacks

  • There are currently no refbacks.




CC BY-SA