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Dynamical Behavior of a New Chaotic System with One Stable Equilibrium

Author

Listed:
  • Vijayakumar M.D.

    (Centre for Materials Research, Chennai Institute of Technology, Chennai 600069, India)

  • Anitha Karthikeyan

    (Electronics and Communications Engineering, Prathyusha Engineering College, Thiruvallur 602025, India)

  • Jozef Zivcak

    (Department of Biomedical Engineering and Measurement, Faculty of Mechanical Engineering, Technical University of Kosice, 040 01 Kosice, Slovakia)

  • Ondrej Krejcar

    (Department of Biomedical Engineering and Measurement, Faculty of Mechanical Engineering, Technical University of Kosice, 040 01 Kosice, Slovakia
    Center for Basic and Applied Research, Faculty of Informatics and Management, University of Hradec Kralove, 500 03 Hradec Kralove, Czech Republic)

  • Hamidreza Namazi

    (Center for Basic and Applied Research, Faculty of Informatics and Management, University of Hradec Kralove, 500 03 Hradec Kralove, Czech Republic
    College of Engineering and Science, Victoria University, Melbourne, VIC 3011, Australia)

Abstract

This paper reports a simple three-dimensional autonomous system with a single stable node equilibrium. The system has a constant controller which adjusts the dynamic of the system. It is revealed that the system exhibits both chaotic and non-chaotic dynamics. Moreover, chaotic or periodic attractors coexist with a single stable equilibrium for some control parameter based on initial conditions. The system dynamics are studied by analyzing bifurcation diagrams, Lyapunov exponents, and basins of attractions. Beyond a fixed-point analysis, a new analysis known as connecting curves is provided. These curves are one-dimensional sets of the points that are more informative than fixed points. These curves are the skeleton of the system, which shows the direction of flow evolution.

Suggested Citation

  • Vijayakumar M.D. & Anitha Karthikeyan & Jozef Zivcak & Ondrej Krejcar & Hamidreza Namazi, 2021. "Dynamical Behavior of a New Chaotic System with One Stable Equilibrium," Mathematics, MDPI, vol. 9(24), pages 1-9, December.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:24:p:3217-:d:701121
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    References listed on IDEAS

    as
    1. Jafari, Sajad & Sprott, J.C., 2013. "Simple chaotic flows with a line equilibrium," Chaos, Solitons & Fractals, Elsevier, vol. 57(C), pages 79-84.
    2. Dhinakaran Veeman & Hayder Natiq & Nadia M. G. Al-Saidi & Karthikeyan Rajagopal & Sajad Jafari & Iqtadar Hussain & Jorge-Antonio Lopez-Renteria, 2021. "A New Megastable Chaotic Oscillator with Blinking Oscillation terms," Complexity, Hindawi, vol. 2021, pages 1-12, April.
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    Cited by:

    1. Sundarapandian Vaidyanathan & Ahmad Taher Azar & Ibrahim A. Hameed & Khaled Benkouider & Esteban Tlelo-Cuautle & Brisbane Ovilla-Martinez & Chang-Hua Lien & Aceng Sambas, 2023. "Bifurcation Analysis, Synchronization and FPGA Implementation of a New 3-D Jerk System with a Stable Equilibrium," Mathematics, MDPI, vol. 11(12), pages 1-22, June.

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