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Dynamics Feature and Synchronization of a Robust Fractional-Order Chaotic System

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  • Xuan-Bing Yang
  • Yi-Gang He
  • Chun-Lai Li

Abstract

Exploring the dynamics feature of robust chaotic system is an attractive yet recent topic of interest. In this paper, we introduce a three-dimensional fractional-order chaotic system. The important finding by analysis is that the position of signal x 3 descends at the speed of 1/ c as the parameter b increases, and the signal amplitude of x 1 , x 2 can be controlled by the parameter m in terms of the power function with the index −1/2. What is more, the dynamics remains constant with the variation of parameters b and m . Consequently, this system can provide rich encoding keys for chaotic communication. By considering the properties of amplitude and position modulation, the partial projective synchronization and partial phase synchronization are realized with linear control scheme. The distribution map of optimal synchronization region in the control-parameter space is charted by defining the power consumption of controller. Numerical simulations are executed to confirm the theoretical analysis.

Suggested Citation

  • Xuan-Bing Yang & Yi-Gang He & Chun-Lai Li, 2018. "Dynamics Feature and Synchronization of a Robust Fractional-Order Chaotic System," Complexity, Hindawi, vol. 2018, pages 1-12, December.
    • Handle: RePEc:hin:complx:8797314
    DOI: 10.1155/2018/8797314
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    References listed on IDEAS

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    1. Kajbaf, Amin & Akhaee, Mohammad Ali & Sheikhan, Mansour, 2016. "Fast synchronization of non-identical chaotic modulation-based secure systems using a modified sliding mode controller," Chaos, Solitons & Fractals, Elsevier, vol. 84(C), pages 49-57.
    2. 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.
    3. Mahmoud, Emad E., 2013. "Modified projective phase synchronization of chaotic complex nonlinear systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 89(C), pages 69-85.
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    1. Runlong Peng & Cuimei Jiang & Rongwei Guo, 2021. "Partial Anti-Synchronization of the Fractional-Order Chaotic Systems through Dynamic Feedback Control," Mathematics, MDPI, vol. 9(7), pages 1-13, March.

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