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Chaos, control and synchronization of a fractional order rotational mechanical system with a centrifugal governor

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  • Ge, Zheng-Ming
  • Jhuang, Wei-Ren

Abstract

Chaos, its control and synchronization for a fractional order rotational mechanical system with a centrifugal governor are studied for both the autonomous and the nonautonomous cases. It is found that chaos exists in the fractional order systems with order less than and more than the number of states of the system. Controlling the chaotic motion of a fractional order system to its equilibrium point is obtained for both the autonomous and the nonautonomous cases. The rotational mechanical systems with the same fractional order and with the different fractional orders are synchronized by linear coupling for both the autonomous and the nonautonomous cases.

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  • Ge, Zheng-Ming & Jhuang, Wei-Ren, 2007. "Chaos, control and synchronization of a fractional order rotational mechanical system with a centrifugal governor," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 270-289.
    • Handle: RePEc:eee:chsofr:v:33:y:2007:i:1:p:270-289
    DOI: 10.1016/j.chaos.2005.12.040
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    References listed on IDEAS

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    1. Lu, Jun Guo, 2006. "Synchronization of a class of fractional-order chaotic systems via a scalar transmitted signal," Chaos, Solitons & Fractals, Elsevier, vol. 27(2), pages 519-525.
    2. Elabbasy, E.M. & Agiza, H.N. & El-Dessoky, M.M., 2005. "Global synchronization criterion and adaptive synchronization for new chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 23(4), pages 1299-1309.
    3. Yassen, M.T., 2005. "Controlling chaos and synchronization for new chaotic system using linear feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 913-920.
    4. Ge, Z.-M. & Cheng, J.-W., 2005. "Chaos synchronization and parameter identification of three time scales brushless DC motor system," Chaos, Solitons & Fractals, Elsevier, vol. 24(2), pages 597-616.
    5. Ge, Zheng-Ming & Lee, Ching-I, 2005. "Control, anticontrol and synchronization of chaos for an autonomous rotational machine system with time-delay," Chaos, Solitons & Fractals, Elsevier, vol. 23(5), pages 1855-1864.
    6. Park, Ju H., 2005. "Chaos synchronization of a chaotic system via nonlinear control," Chaos, Solitons & Fractals, Elsevier, vol. 25(3), pages 579-584.
    7. Ge, Zheng-Ming & Chen, Yen-Sheng, 2005. "Adaptive synchronization of unidirectional and mutual coupled chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 881-888.
    8. Ahmad, Wajdi M., 2005. "Hyperchaos in fractional order nonlinear systems," Chaos, Solitons & Fractals, Elsevier, vol. 26(5), pages 1459-1465.
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    Cited by:

    1. Nazim I Mahmudov & Sameer Bawaneh & Areen Al-Khateeb, 2019. "On a Coupled System of Fractional Differential Equations with Four Point Integral Boundary Conditions," Mathematics, MDPI, vol. 7(3), pages 1-14, March.
    2. Deng, Hongmin & Li, Tao & Wang, Qionghua & Li, Hongbin, 2009. "A fractional-order hyperchaotic system and its synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 962-969.
    3. Surendar, R. & Muthtamilselvan, M. & Ahn, Kyubok, 2024. "Stochastic disturbance with finite-time chaos stabilization and synchronization for a fractional-order nonautonomous hybrid nonlinear complex system via a sliding mode control," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    4. Ahmad, Bashir & Ntouyas, Sotiris K. & Alsaedi, Ahmed, 2016. "On a coupled system of fractional differential equations with coupled nonlocal and integral boundary conditions," Chaos, Solitons & Fractals, Elsevier, vol. 83(C), pages 234-241.
    5. Yang, Yanling & Wang, Qiubao, 2023. "Capture of stochastic P-bifurcation in a delayed mechanical centrifugal governor," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    6. Longfei Lin & Yansheng Liu & Daliang Zhao, 2021. "Study on Implicit-Type Fractional Coupled System with Integral Boundary Conditions," Mathematics, MDPI, vol. 9(4), pages 1-15, February.
    7. Longfei Lin & Yansheng Liu & Daliang Zhao, 2021. "Controllability of Impulsive ψ -Caputo Fractional Evolution Equations with Nonlocal Conditions," Mathematics, MDPI, vol. 9(12), pages 1-14, June.
    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. Yu, Yongguang & Li, Han-Xiong, 2008. "The synchronization of fractional-order Rössler hyperchaotic systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(5), pages 1393-1403.

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