Experimental Realization of a Multiscroll Chaotic Oscillator with Optimal Maximum Lyapunov Exponent

Nowadays, different kinds of experimental realizations of chaotic oscillators have been already presented in the literature. However, those realizations do not consider the value of the maximum Lyapunov exponent, which gives a quantitative measure of the grade of unpredictability of chaotic systems....

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Bibliographic Details
Published in:TheScientificWorld 2014-01, Vol.2014 (2014), p.1-16
Main Authors: Sanchez-Sanchez, Mauro, Carbajal-Gomez, Victor Hugo, Pano-Azucena, Ana Dalia, Tlelo-Cuautle, Esteban
Format: Article
Language:English
Subjects:
Algorithms
Analysis
Chaos theory
Electronics - methods
Genetic algorithms
Liapunov functions
Mathematical models
Models, Theoretical
Nonlinear Dynamics
Oscillometry - methods
Potentiometers
Receivers & amplifiers
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Summary:Nowadays, different kinds of experimental realizations of chaotic oscillators have been already presented in the literature. However, those realizations do not consider the value of the maximum Lyapunov exponent, which gives a quantitative measure of the grade of unpredictability of chaotic systems. That way, this paper shows the experimental realization of an optimized multiscroll chaotic oscillator based on saturated function series. First, from the mathematical description having four coefficients (a, b, c, d1), an optimization evolutionary algorithm varies them to maximize the value of the positive Lyapunov exponent. Second, a realization of those optimized coefficients using operational amplifiers is given. Herein a, b, c, d1 are implemented with precision potentiometers to tune up to four decimals of the coefficients having the range between 0.0001 and 1.0000. Finally, experimental results of the phase-space portraits for generating from 2 to 10 scrolls are listed to show that their associated value for the optimal maximum Lyapunov exponent increases by increasing the number of scrolls, thus guaranteeing a more complex chaotic behavior.
ISSN:2356-6140
1537-744X
1537-744X
DOI:10.1155/2014/303614