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Stability and chaos in the fractional Chen system

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  • Čermák, Jan
  • Nechvátal, Luděk

Abstract

The paper provides a theoretical analysis of some local bifurcations in the fractional Chen system. Contrary to the integer-order case, basic bifurcation properties of the fractional Chen system are shown to be qualitatively different from those described previously for the fractional Lorenz system. Further, the fractional Hopf bifurcation in the Chen system is expressed rigorously with respect to general entry parameters. Based on these observations, some particularities of the fractional dynamics of the Chen system are documented and its chaotic behavior for low derivative orders is discussed.

Suggested Citation

  • Čermák, Jan & Nechvátal, Luděk, 2019. "Stability and chaos in the fractional Chen system," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 24-33.
    • Handle: RePEc:eee:chsofr:v:125:y:2019:i:c:p:24-33
    DOI: 10.1016/j.chaos.2019.05.007
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    References listed on IDEAS

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    1. Wen, Shao-Fang & Shen, Yong-Jun & Yang, Shao-Pu & Wang, Jun, 2017. "Dynamical response of Mathieu–Duffing oscillator with fractional-order delayed feedback," Chaos, Solitons & Fractals, Elsevier, vol. 94(C), pages 54-62.
    2. Deshpande, Amey S. & Daftardar-Gejji, Varsha & Sukale, Yogita V., 2017. "On Hopf bifurcation in fractional dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 98(C), pages 189-198.
    3. Lu, Jun Guo & Chen, Guanrong, 2006. "A note on the fractional-order Chen system," Chaos, Solitons & Fractals, Elsevier, vol. 27(3), pages 685-688.
    4. Garrappa, Roberto, 2015. "Trapezoidal methods for fractional differential equations: Theoretical and computational aspects," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 110(C), pages 96-112.
    5. Wang, Zhen & Xie, Yingkang & Lu, Junwei & Li, Yuxia, 2019. "Stability and bifurcation of a delayed generalized fractional-order prey–predator model with interspecific competition," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 360-369.
    6. Leonov, G.A. & Kuznetsov, N.V., 2015. "On differences and similarities in the analysis of Lorenz, Chen, and Lu systems," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 334-343.
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    Cited by:

    1. Alidousti, J. & Eskandari, Z. & Avazzadeh, Z., 2020. "Generic and symmetric bifurcations analysis of a three dimensional economic model," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).

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