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

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

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.

Suggested Citation

  • Silva-Juárez, Alejandro & Tlelo-Cuautle, Esteban & de la Fraga, Luis Gerardo & Li, Rui, 2021. "Optimization of the Kaplan-Yorke dimension in fractional-order chaotic oscillators by metaheuristics," Applied Mathematics and Computation, Elsevier, vol. 394(C).
    • Handle: RePEc:eee:apmaco:v:394:y:2021:i:c:s0096300320307840
    DOI: 10.1016/j.amc.2020.125831
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    References listed on IDEAS

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    1. Ping Zhou & Meihua Ke, 2018. "An Integer-Order Memristive System with Two- to Four-Scroll Chaotic Attractors and Its Fractional-Order Version with a Coexisting Chaotic Attractor," Complexity, Hindawi, vol. 2018, pages 1-7, July.
    2. Li, Chunguang & Chen, Guanrong, 2004. "Chaos and hyperchaos in the fractional-order Rössler equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 341(C), pages 55-61.
    3. Yu, Yongguang & Li, Han-Xiong & Wang, Sha & Yu, Junzhi, 2009. "Dynamic analysis of a fractional-order Lorenz chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1181-1189.
    4. Xikui Hu & Ping Zhou, 2020. "Coexisting Three-Scroll and Four-Scroll Chaotic Attractors in a Fractional-Order System by a Three-Scroll Integer-Order Memristive Chaotic System and Chaos Control," Complexity, Hindawi, vol. 2020, pages 1-7, January.
    5. Tavazoei, Mohammad Saleh & Haeri, Mohammad, 2009. "A note on the stability of fractional order systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(5), pages 1566-1576.
    6. Liu, Xianggang & Ma, Li, 2020. "Chaotic vibration, bifurcation, stabilization and synchronization control for fractional discrete-time systems," Applied Mathematics and Computation, Elsevier, vol. 385(C).
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    Cited by:

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