Optimization of the Kaplan-Yorke dimension in fractional-order chaotic oscillators by metaheuristics

Alejandro Silva-Juárez, Esteban Tlelo-Cuautle, Luis Gerardo de la Fraga and Rui Li

Applied Mathematics and Computation, 2021, vol. 394, issue C

Abstract: The optimization of the Kaplan-Yorke dimension (DKY) of fractional-order chaotic oscillators (FOCOs) is shown herein by applying two metaheuristics, namely: differential evolution and particle swarm optimization algorithms. The optimization process is performed in two stages, and the cases of study are five commensurate (all derivatives have the same fractional-order) and incommensurate (all derivatives have different fractional-order) FOCOs. The first optimization stage evaluates the equilibrium points and eigenvalues of the individuals or particles to verify if they accomplish the minimum fractional-order value to guarantee chaotic behavior. The individuals or particles accomplishing this requirement are passed to the second optimization stage evaluating their DKY. This saves computing time because the individuals or particles that do not accomplish the minimum fractional-order value, are not simulated in the time domain. We show that this optimization approach generates feasible values of the parameters of the FOCOs, providing better DKY values compared to the ones already reported in the literature.

Keywords: Chaos; Fractional order chaotic oscillator; Differential evolution; Particle swarm optimization; Lyapunov exponent; Kaplan-Yorke dimension (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:394:y:2021:i:c:s0096300320307840

DOI: 10.1016/j.amc.2020.125831

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