Abstract
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.
Highlights
Chaos is a multidisciplinary research area that is being ubiquitous in all engineering areas, such as electronics, control, communication, and security
In electronics we are interested in the realization of chaotic oscillators, in which mathematical descriptions have three main characteristics: a chaotic oscillator is sensitive to initial conditions, it is nonperiodic, and it is deterministic, because the coefficients of its mathematical description are known [4]
In continuous-time chaotic oscillators the number of state variables determines the number of Lyapunov exponents, so that for a third order dynamical system, the three Lyapunov exponents for generating chaos should be negative, zero, and positive
Summary
Chaos is a multidisciplinary research area that is being ubiquitous in all engineering areas, such as electronics, control, communication, and security. Engineers are interested in the analysis, realization, and application of chaos [1,2,3]. A measure for quantifying chaos in dynamical systems is by computing the value of the Lyapunov exponents, from which one gets information on their grade of unpredictability [5]. In continuous-time chaotic oscillators the number of state variables determines the number of Lyapunov exponents, so that for a third order dynamical system, the three Lyapunov exponents for generating chaos should be negative, zero, and positive. Higher order dynamical systems should possess at least one positive Lyapunov exponent to guarantee chaotic regime.
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