Abstract
Guaranteeing chaotic behavior in integer and fractional-order chaotic systems for long-time simulation is a challenge. This chapter details the requirements for a correct time simulation of an integer and fractional-order chaotic system, in order to evaluate the Lyapunov exponents and Kaplan–Yorke dimension. Using TISEAN or Wolf’s method one can compute both Lyapunov exponents and Kaplan–Yorke dimension within an optimization loop that can be performed by applying metaheuristics. Differential evolution and particle swarm optimization algorithms are applied herein to optimize the positive Lyapunov exponent and Kaplan–Yorke dimension of integer and fractional-order chaotic oscillators.
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Tlelo-Cuautle, E., Dalia Pano-Azucena, A., Guillén-Fernández, O., Silva-Juárez, A. (2020). Characterization and Optimization of Fractional-Order Chaotic Systems. In: Analog/Digital Implementation of Fractional Order Chaotic Circuits and Applications. Springer, Cham. https://doi.org/10.1007/978-3-030-31250-3_3
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DOI: https://doi.org/10.1007/978-3-030-31250-3_3
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