IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v394y2021ics0096300320307840.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300320307840
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2020.125831?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    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).
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Du, Chuanhong & Liu, Licai & Zhang, Zhengping & Yu, Shixing, 2022. "A mem-element Wien-Bridge circuit with amplitude modulation and three kinds of offset boosting," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    2. Jiri Petrzela & Miroslav Rujzl, 2022. "Chaotic Oscillations in Cascoded and Darlington-Type Amplifier Having Generalized Transistors," Mathematics, MDPI, vol. 10(3), pages 1-25, February.
    3. Mei-Qi, Wang & Wen-Li, Ma & En-Li, Chen & Yu-Jian, Chang & Cui-Yan, Wang, 2022. "Principal resonance analysis of piecewise nonlinear oscillator with fractional calculus," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Laarem, Guessas, 2021. "A new 4-D hyper chaotic system generated from the 3-D Rösslor chaotic system, dynamical analysis, chaos stabilization via an optimized linear feedback control, it’s fractional order model and chaos sy," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    2. Shukla, Manoj Kumar & Sharma, B.B., 2017. "Backstepping based stabilization and synchronization of a class of fractional order chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 274-284.
    3. Deepika, Deepika & Kaur, Sandeep & Narayan, Shiv, 2018. "Uncertainty and disturbance estimator based robust synchronization for a class of uncertain fractional chaotic system via fractional order sliding mode control," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 196-203.
    4. Munoz-Pacheco, J.M. & Zambrano-Serrano, E. & Volos, Ch. & Tacha, O.I. & Stouboulos, I.N. & Pham, V.-T., 2018. "A fractional order chaotic system with a 3D grid of variable attractors," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 69-78.
    5. Ge, Zheng-Ming & Yi, Chang-Xian, 2007. "Chaos in a nonlinear damped Mathieu system, in a nano resonator system and in its fractional order systems," Chaos, Solitons & Fractals, Elsevier, vol. 32(1), pages 42-61.
    6. Hanshuo Qiu & Xiangzi Zhang & Huaixiao Yue & Jizhao Liu, 2023. "A Novel Eighth-Order Hyperchaotic System and Its Application in Image Encryption," Mathematics, MDPI, vol. 11(19), pages 1-29, September.
    7. Hajipour, Ahamad & Hajipour, Mojtaba & Baleanu, Dumitru, 2018. "On the adaptive sliding mode controller for a hyperchaotic fractional-order financial system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 497(C), pages 139-153.
    8. Zambrano-Serrano, Ernesto & Bekiros, Stelios & Platas-Garza, Miguel A. & Posadas-Castillo, Cornelio & Agarwal, Praveen & Jahanshahi, Hadi & Aly, Ayman A., 2021. "On chaos and projective synchronization of a fractional difference map with no equilibria using a fuzzy-based state feedback control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 578(C).
    9. Tam, Lap Mou & Si Tou, Wai Meng, 2008. "Parametric study of the fractional-order Chen–Lee system," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 817-826.
    10. Wang, Fei & Yang, Yongqing & Hu, Manfeng & Xu, Xianyun, 2015. "Projective cluster synchronization of fractional-order coupled-delay complex network via adaptive pinning control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 434(C), pages 134-143.
    11. Soliman, Nancy S. & Tolba, Mohammed F. & Said, Lobna A. & Madian, Ahmed H. & Radwan, Ahmed G., 2019. "Fractional X-shape controllable multi-scroll attractor with parameter effect and FPGA automatic design tool software," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 292-307.
    12. Cruz-Victoria, Juan C. & Martínez-Guerra, Rafael & Pérez-Pinacho, Claudia A. & Gómez-Cortés, Gian Carlo, 2015. "Synchronization of nonlinear fractional order systems by means of PIrα reduced order observer," Applied Mathematics and Computation, Elsevier, vol. 262(C), pages 224-231.
    13. Lu, Jun Guo & Chen, Guanrong, 2006. "A note on the fractional-order Chen system," Chaos, Solitons & Fractals, Elsevier, vol. 27(3), pages 685-688.
    14. Zheng, Yongai & Ji, Zhilin, 2016. "Predictive control of fractional-order chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 307-313.
    15. Gao, Xin & Yu, Juebang, 2005. "Synchronization of two coupled fractional-order chaotic oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 26(1), pages 141-145.
    16. Sheu, Long-Jye & Chen, Hsien-Keng & Chen, Juhn-Horng & Tam, Lap-Mou & Chen, Wen-Chin & Lin, Kuang-Tai & Kang, Yuan, 2008. "Chaos in the Newton–Leipnik system with fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 36(1), pages 98-103.
    17. Peng, Guojun & Jiang, Yaolin & Chen, Fang, 2008. "Generalized projective synchronization of fractional order chaotic systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(14), pages 3738-3746.
    18. Petráš, Ivo, 2008. "A note on the fractional-order Chua’s system," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 140-147.
    19. Muñoz-Vázquez, Aldo Jonathan & Ortiz-Moctezuma, Manuel Benjamín & Sánchez-Orta, Anand & Parra-Vega, Vicente, 2019. "Adaptive robust control of fractional-order systems with matched and mismatched disturbances," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 162(C), pages 85-96.
    20. Li, Zengshan & Chen, Diyi & Ma, Mengmeng & Zhang, Xinguang & Wu, Yonghong, 2017. "Feigenbaum's constants in reverse bifurcation of fractional-order Rössler system," Chaos, Solitons & Fractals, Elsevier, vol. 99(C), pages 116-123.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:394:y:2021:i:c:s0096300320307840. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.