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Coexisting Attractor in a Gyrostat Chaotic System via Basin of Attraction and Synchronization of Two Nonidentical Mechanical Systems

Author

Listed:
  • Muhammad Marwan

    (College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, China)

  • Vagner Dos Santos

    (Department of Mathematics and Statistics, State University of Ponta Grossa, Ponta Grossa 84030-900, Paraná, Brazil
    Universitário Faculdade de Telêmaco Borba UNIFATEB, Telêmaco Borba 84266-010, Paraná, Brazil)

  • Muhammad Zainul Abidin

    (College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, China)

  • Anda Xiong

    (School of Physics and Astronomy, University of Birmingham, Birmingham B15 2TT, UK)

Abstract

This paper is divided into two main portions. First, we look at basins of attraction as a tool with a unique set of characteristics for discussing multistability and coexisting attractors in a gyrostat chaotic system. For the validation of coexisting attractors in different basins, several approaches such as bifurcation diagrams, Lyapunov exponents, and the Poincaré section are applied. The second half of the study synchronizes two mechanical chaotic systems using a novel controller, with gyrostat and quadrotor unmanned aerial vehicle (QUAV) chaotic systems acting as master and slave systems, respectively. The error dynamical system and the parameter updated law are built using Lyapunov’s theory, and it is discovered that under certain parametric conditions, the trajectories of the QUAV chaotic system overlap and begin to match the features of the gyrostat chaotic system.

Suggested Citation

  • Muhammad Marwan & Vagner Dos Santos & Muhammad Zainul Abidin & Anda Xiong, 2022. "Coexisting Attractor in a Gyrostat Chaotic System via Basin of Attraction and Synchronization of Two Nonidentical Mechanical Systems," Mathematics, MDPI, vol. 10(11), pages 1-15, June.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:11:p:1914-:d:830883
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    References listed on IDEAS

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    1. Long Ding & Li Cui & Fei Yu & Jie Jin & Guillermo Huerta Cuellar, 2021. "Basin of Attraction Analysis of New Memristor-Based Fractional-Order Chaotic System," Complexity, Hindawi, vol. 2021, pages 1-9, April.
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    3. Xia Lu, 2020. "A Financial Chaotic System Control Method Based on Intermittent Controller," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-12, March.
    4. John Alexander Taborda & Fabiola Angulo, 2015. "Computing and Controlling Basins of Attraction in Multistability Scenarios," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-13, December.
    5. Sabir, Muhammad & Marwan, Muhammad & Ahmad, Salman & Fiaz, Muhammad & Khan, Farhan, 2020. "Observer and descriptor satisfying incremental quadratic constraint for class of chaotic systems and its applications in a quadrotor chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    6. Ercan Köse & Aydın Mühürcü, 2018. "Comparative Controlling of the Lorenz Chaotic System Using the SMC and APP Methods," Mathematical Problems in Engineering, Hindawi, vol. 2018, pages 1-9, December.
    7. A. Brett & M. R. S. Kulenović, 2015. "Basins of Attraction for Two-Species Competitive Model with Quadratic Terms and the Singular Allee Effect," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-16, January.
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    9. Guoyuan Qi & Xiaogang Yang, 2019. "Modeling of a Chaotic Gyrostat System and Mechanism Analysis of Dynamics Using Force and Energy," Complexity, Hindawi, vol. 2019, pages 1-13, July.
    10. Chen, Yun & Xu, Yanyi & Lin, Qian & Zhang, Xiyong, 2020. "Model and criteria on the global finite-time synchronization of the chaotic gyrostat systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 178(C), pages 515-533.
    11. Omar Guillén-Fernández & Ashley Meléndez-Cano & Esteban Tlelo-Cuautle & Jose Cruz Núñez-Pérez & Jose de Jesus Rangel-Magdaleno, 2019. "On the synchronization techniques of chaotic oscillators and their FPGA-based implementation for secure image transmission," PLOS ONE, Public Library of Science, vol. 14(2), pages 1-34, February.
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    Cited by:

    1. Yassine Bouteraa & Javad Mostafaee & Mourad Kchaou & Rabeh Abbassi & Houssem Jerbi & Saleh Mobayen, 2022. "A New Simple Chaotic System with One Nonlinear Term," Mathematics, MDPI, vol. 10(22), pages 1-17, November.
    2. Karawanich, Khunanon & Prommee, Pipat, 2022. "High-complex chaotic system based on new nonlinear function and OTA-based circuit realization," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).

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