International Journal of Scientific & Technology Research

Home About Us Scope Editorial Board Blog/Latest News Contact Us
10th percentile
Powered by  Scopus
Scopus coverage:
Nov 2018 to May 2020


IJSTR >> Volume 3- Issue 7, July 2014 Edition

International Journal of Scientific & Technology Research  
International Journal of Scientific & Technology Research

Website: http://www.ijstr.org

ISSN 2277-8616

Numerical Calculation Of Lyapunov Exponents In Various Nonlinear Chaotic Systems

[Full Text]



Joan Jani, Partizan Malkaj



Index Terms: chaos, nonlinear sience, lyapunov exponents



Abstract: In this paper we study the meaning and importance of Lyapunov exponents through methods of analysis of experimental data applied in physics, and especially in chaotic circuits. The Lyapunov exponents play a very important role in detecting chaos, which occurs in many areas of science and technology. So, the question belongs to the theory of chaotic dynamical systems and generally all dynamical systems, which should analyzed correctly and accurately to obtain the correct conclusions regards Lyapunov exponents. The purpose of the study is to find the Lyapunov exponents for various dynamical systems and the explanation of the results for the dynamic behavior of each system. We also present applications science where Lyapunov exponents play an important role in explaining the main algorithms to calculate these exponents under different implementation and different computer packages.



M. P. Hanias, I. L. Giannis, and G. S. Tombras, “Chaotic operation by a single transistor circuit in the reverse active region.,” Chaos, vol. 20, no. 1, p. 013105, Mar. 2010.

[2] A. Ugulava and L. Chotorlishvili, “Chaos, Fractals and Quantum Poincaré Recurrences in Diamagnetic Kepler Problem,” … Phys. Lett. B, vol. 0, pp. 1–19, Aug. 2007.

[3] K. T. Alligood, T. D. Sauer, J. a. Yorke, and J. D. Crawford, Chaos: An Introduction to Dynamical Systems, vol. 50. Springer, 1997, p. 67.

[4] R. Rollins and E. Hunt, “Exactly Solvable Model of a Physical System Exhibiting Universal Chaotic Behavior,” Phys. Rev. Lett., vol. 49, no. 18, pp. 1295–1298, Nov. 1982.

[5] R. Hegger, H. Kantz, and T. Schreiber, “Practical implementation of nonlinear time series methods: The TISEAN package,” Sep. 1998.

[6] A. Wolf, J. Swift, H. Swinney, and J. Vastano, “Determining Lyapunov exponents from a time series,” Phys. D Nonlinear …, pp. 285–317, 1985.

[7] M. T. Rosenstein, J. J. Collins, and C. J. De Luca, “A practical method for calculating largest Lyapunov exponents from small data sets,” Phys. D Nonlinear Phenom., vol. 65, no. 1–2, pp. 117–134, May 1993.

[8] R. May and G. Oster, “Bifurcations and dynamic complexity in simple ecological models,” Am. Nat., 1976.