Modeling and Simulation of a Chaotic Oscillator Using Mathematica

Authors

  • Mohamed Mostafa Saied Independent Researcher, Giza, Cairo, Egypt

Abstract

This paper suggests a modified methodology for the modeling and simulation of a chaotic oscillator. Its analysis and the pertinent results of an efficient Mathematica simulation program dealing with a typical Chua's circuit are presented and discussed. The derived computer code is based on the application of state-variables in the time domain. The program yields the circuit’s currents and voltages and indicates their sensitivities to changes in the numerical values of the circuit elements. An efficient and accurate curve fitting technique dealing with the current-voltage relationship of the Chua’s diode (NR) is adopted. It is based on an assumed combination of polynomial and exponential terms. This will be followed by the numerical solution of the resulting system of differential-algebraic equations using Mathematica in order to simulate the behavior of a chaotic oscillator. The results of several case studies are presented and discussed.

Author Biography

  • Mohamed Mostafa Saied, Independent Researcher, Giza, Cairo, Egypt

    Independent Researcher, Full Professor, Electrical Engineering 

    B.Sc. , Electrical Engineering, Cairo University (1965)

    Dipl.-Ing. , Electrical Engineering, RWTH, Aachen University, Germany (1970)

    Dr.-Ing. , Electrical Engineering, RWTH, Aachen University, Germany (1974)

    Full Professor, EE, Kuwait University (1983-2009)

    Visiting Full Professor, EE, Kuwait University (1998-1099)

    Pepartment Chairman, EE, Kuwait University (2004-2009)

     

References

Michael P. Kennedy. Robust OP AMP Realization of Chua’s Circuit. Frequenz: 1992; 46 ( ¾): 66-80.

Leonardo Antonio Borges TorresLuis Antonio Aguirre. Inductorless Chua's circuit. Electronics Letters:2000; 36(23):1915 – 1916

Morgul. RC realization of Chua's circuit family. IEEE Transactions on Circuits and Systems: 2000; 47(9): 14-24.

E. Tlelo-Cuautle, M.A. Duarte-Villasenor. Designing Chua’s circuit from the behavioral to the transistor level of abstraction. J. Applied Mathematics and Computation: 2007; 184:715-720

Esteban Tlelo-Cuautle, Jesus-Manuel Mufioz-Pacheco. Numerical Simulation of Chua's Circuit Oriented to Circuit Synthesis. Internl. Journal of Nonlinear Sciences and Numerical Simulation : 2007; 8(2):249-256

Ricai Killic. A Practical Guide for Studying Chua's Circuits. , World Scientific: March 2010.

Valentin Siderskiy and Vikram Kapila. Parameter Matching Using Adaptive Synchronization of Two Chua's Oscillators. International Journal of Bifurcation and Chaos: 2014; 24(11): 1430032

Leon O. Chua, Chai Wah Wu, Anshan Huang et al. A Universal Circuit for Studying and Generating Chaos- Part I: Routes to Chaos. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications:1993; 40 (10):732 - 744

Wolfram Mathematica Tutorial Collection. Advanced Numerical Differential Equation Solving. in Mathematica. Wolfram Research. 2008

Downloads

Published

2021-05-26

Issue

Vol. 11 No. 1 (2021)

Section

Research Article

License

Journal Title:

Title of the Paper:

Corresponding Author’s Information:

Name: Address:

E-mail:

Contact Number:

It is herein agreed that: The copyright to the above-listed unpublished and original article is transferred to STM Journals.

This copyright transfer covers the exclusive right to reproduce and distribute the contribution, including reprints, translations, photographic reproductions, microform, electronic form (offline, online), or any other reproductions of similar nature.

I/We declare that above manuscript is not published already in part or whole (except in the form of abstract) in any journal or magazine for private or public circulation, and, is not under consideration of publication elsewhere.

 I/ We warrant(s) that his/her/their contribution is original, except for such excerpts from copyrighted works as may be included with the permission of the copyright holder and author thereof, that it contains no libelous statements, and does not infringe on any copyright, trademark, patent, statutory right, or propriety right of others.

I/We will not publish his/her/their above said contribution anywhere else without the prior written permission of the publisher unless it has been changed substantially. I/We also agree to the authorship of the article in the following order: Author(s) Name Signature(s)

1. ________________

2. ________________

3. ________________

4. ________________

The author(s) agree to the terms of this Copyright Notice, which will apply to this submission if and when it is published by this journal (comments if any to the editor can be added below).