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Global dynamical analysis of the integer and fractional 4D hyperchaotic Rabinovich system

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  • Ren, Lei
  • Lin, Ming-Hung
  • Abdulwahab, Abdulkareem
  • Ma, Jun
  • Saberi-Nik, Hassan

Abstract

In this paper, the dynamical behavior of integer and fractional 4D hyperchaotic Rabinovich system is studied. We use the Lagrange coefficient method to solve an optimization problem analytically so that find an accurate ultimate bound set (UBS) for the 4D hyperchaotic Rabinovich system. Furthermore, bifurcation diagrams, Lyapunov exponents, global attractive sets (GASs), and positive invariant sets (PISs) of the fractional-order system are studied. Finally, using the Mittag-Leffler function and Lyapunov function method, the Mittag-Leffler GAS and Mittag-Leffler PIS of the proposed system are estimated. Our investigations indicate that there is a close relationship between changing the parameters and the dynamical behavior of the system, Hamilton energy consumption and changing the bound of the variables. The corresponding boundedness is numerically verified to show the effectiveness of the theoretical analysis.

Suggested Citation

  • Ren, Lei & Lin, Ming-Hung & Abdulwahab, Abdulkareem & Ma, Jun & Saberi-Nik, Hassan, 2023. "Global dynamical analysis of the integer and fractional 4D hyperchaotic Rabinovich system," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    • Handle: RePEc:eee:chsofr:v:169:y:2023:i:c:s0960077923001765
    DOI: 10.1016/j.chaos.2023.113275
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    1. Gao, Wei & Yan, Li & Saeedi, Mohammadhossein & Saberi Nik, Hassan, 2018. "Ultimate bound estimation set and chaos synchronization for a financial risk system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 154(C), pages 19-33.
    2. Wang, Shaojie & He, Shaobo & Yousefpour, Amin & Jahanshahi, Hadi & Repnik, Robert & Perc, Matjaž, 2020. "Chaos and complexity in a fractional-order financial system with time delays," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    3. Tavazoei, Mohammad Saleh & Haeri, Mohammad, 2008. "Synchronization of chaotic fractional-order systems via active sliding mode controller," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(1), pages 57-70.
    4. Jiezhi Wang & Qing Zhang & Zengqiang Chen & Hang Li, 2014. "Ultimate Bound of a 3D Chaotic System and Its Application in Chaos Synchronization," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-9, July.
    5. Peng, Qiu & Jian, Jigui, 2021. "Estimating the ultimate bounds and synchronization of fractional-order plasma chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    6. Bonyah, Ebenezer, 2018. "Chaos in a 5-D hyperchaotic system with four wings in the light of non-local and non-singular fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 316-331.
    7. Mahmoud, Emad E. & Trikha, Pushali & Jahanzaib, Lone Seth & Almaghrabi, Omar A., 2020. "Dynamical analysis and chaos control of the fractional chaotic ecological model," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    8. Chunlai Li & Jing Zhang, 2016. "Synchronisation of a fractional-order chaotic system using finite-time input-to-state stability," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(10), pages 2440-2448, July.
    9. Zhou, Ping & Hu, Xikui & Zhu, Zhigang & Ma, Jun, 2021. "What is the most suitable Lyapunov function?," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    10. Jiang, Jingfei & Chen, Huatao & Guirao, Juan L.G. & Cao, Dengqing, 2019. "Existence of the solution and stability for a class of variable fractional order differential systems," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 269-274.
    11. Wang, Haijun & Dong, Guili, 2019. "New dynamics coined in a 4-D quadratic autonomous hyper-chaotic system," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 272-286.
    12. David, S.A. & Machado, J.A.T. & Quintino, D.D. & Balthazar, J.M., 2016. "Partial chaos suppression in a fractional order macroeconomic model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 122(C), pages 55-68.
    13. Xinquan Zhao & Feng Jiang & Zhigang Zhang & Junhao Hu, 2013. "A New Series of Three-Dimensional Chaotic Systems with Cross-Product Nonlinearities and Their Switching," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-14, February.
    14. Chien, Fengsheng & Inc, Mustafa & Yosefzade, Hamidreza & Saberi Nik, Hassan, 2021. "Predicting the chaos and solution bounds in a complex dynamical system," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    15. Ping Zhou & Kun Huang & Chun-de Yang, 2013. "A Fractional-Order Chaotic System with an Infinite Number of Equilibrium Points," Discrete Dynamics in Nature and Society, Hindawi, vol. 2013, pages 1-6, April.
    16. Li, Damei & Wu, Xiaoqun & Lu, Jun-an, 2009. "Estimating the ultimate bound and positively invariant set for the hyperchaotic Lorenz–Haken system," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1290-1296.
    17. Mahmoud, Gamal M. & Arafa, Ayman A. & Abed-Elhameed, Tarek M. & Mahmoud, Emad E., 2017. "Chaos control of integer and fractional orders of chaotic Burke–Shaw system using time delayed feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 680-692.
    18. Xu, Beibei & Chen, Diyi & Zhang, Hao & Wang, Feifei, 2015. "Modeling and stability analysis of a fractional-order Francis hydro-turbine governing system," Chaos, Solitons & Fractals, Elsevier, vol. 75(C), pages 50-61.
    19. Yang, Yingjuan & Qi, Guoyuan, 2018. "Mechanical analysis and bound of plasma chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 108(C), pages 187-195.
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