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Complex Dynamics of the Fractional-Order Rössler System and Its Tracking Synchronization Control

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  • Huihai Wang
  • Shaobo He
  • Kehui Sun

Abstract

Numerical analysis of fractional-order chaotic systems is a hot topic of recent years. The fractional-order Rössler system is solved by a fast discrete iteration which is obtained from the Adomian decomposition method (ADM) and it is implemented on the DSP board. Complex dynamics of the fractional-order chaotic system are analyzed by means of Lyapunov exponent spectra, bifurcation diagrams, and phase diagrams. It shows that the system has rich dynamics with system parameters and the derivative order . Moreover, tracking synchronization controllers are theoretically designed and numerically investigated. The system can track different signals including chaotic signals from the fractional-order master system and constant signals. It lays a foundation for the application of the fractional-order Rössler system.

Suggested Citation

  • Huihai Wang & Shaobo He & Kehui Sun, 2018. "Complex Dynamics of the Fractional-Order Rössler System and Its Tracking Synchronization Control," Complexity, Hindawi, vol. 2018, pages 1-13, December.
    • Handle: RePEc:hin:complx:4019749
    DOI: 10.1155/2018/4019749
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    Cited by:

    1. Laarem, Guessas, 2021. "A new 4-D hyper chaotic system generated from the 3-D Rösslor chaotic system, dynamical analysis, chaos stabilization via an optimized linear feedback control, it’s fractional order model and chaos sy," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    2. Shuai Li & Chengdai Huang & Xinyu Song, 2019. "Bifurcation Based-Delay Feedback Control Strategy for a Fractional-Order Two-Prey One-Predator System," Complexity, Hindawi, vol. 2019, pages 1-13, April.

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