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On Hopf bifurcation in fractional dynamical systems

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  • Deshpande, Amey S.
  • Daftardar-Gejji, Varsha
  • Sukale, Yogita V.

Abstract

Fractional order dynamical systems admit chaotic solutions and the chaos disappears when the fractional order is reduced below a threshold value [1]. Thus the order of the dynamical system acts as a chaos controlling parameter. Hence it is important to study the fractional order dynamical systems and chaos. Study of fractional order dynamical systems is still in its infancy and many aspects are yet to be explored.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:98:y:2017:i:c:p:189-198
    DOI: 10.1016/j.chaos.2017.03.034
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    References listed on IDEAS

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    1. Li, Chunguang & Chen, Guanrong, 2004. "Chaos and hyperchaos in the fractional-order Rössler equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 341(C), pages 55-61.
    2. Singh, Piyush Pratap & Singh, Jay Prakash & Roy, B.K., 2014. "Synchronization and anti-synchronization of Lu and Bhalekar–Gejji chaotic systems using nonlinear active control," Chaos, Solitons & Fractals, Elsevier, vol. 69(C), pages 31-39.
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    Cited by:

    1. Deshpande, Amey S. & Daftardar-Gejji, Varsha, 2017. "On disappearance of chaos in fractional systems," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 119-126.
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    3. Yang, Jing & Hou, Xiaorong & Li, Xiaoxue & Luo, Min, 2022. "A parameter space method for analyzing Hopf bifurcation of fractional-order nonlinear systems with multiple-parameter," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    4. Eshaghi, Shiva & Khoshsiar Ghaziani, Reza & Ansari, Alireza, 2020. "Hopf bifurcation, chaos control and synchronization of a chaotic fractional-order system with chaos entanglement function," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 172(C), pages 321-340.
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