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A parameter space method for analyzing Hopf bifurcation of fractional-order nonlinear systems with multiple-parameter

Author

Listed:
  • Yang, Jing
  • Hou, Xiaorong
  • Li, Xiaoxue
  • Luo, Min

Abstract

Hopf bifurcation analysis of fractional-order nonlinear systems with multiple-parameter is discussed in this paper. The regions and boundaries corresponding to Hopf bifurcation conditions are described in parameter space. Based on cylindrical algebraic decomposition, the parameter space is decomposed into finite number of connected regions by some boundaries. Then parameter space method is proposed to determine stable parameter region and Hopf bifurcation parameter hypersurface. One example illustrates the effectiveness of the method.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:155:y:2022:i:c:s0960077921010687
    DOI: 10.1016/j.chaos.2021.111714
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    References listed on IDEAS

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    1. 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.
    2. Jinbo Lu & Xiaorong Hou & Min Luo, 2015. "Parametric Controller Design of Hopf Bifurcation System," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-10, December.
    3. Zhong Cao & Xiaorong Hou, 2014. "A Symbolic Computation Approach to Parameterizing Controller for Polynomial Hamiltonian Systems," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-8, June.
    4. Jinglei Tian & Yongguang Yu & Hu Wang, 2014. "Stability and Bifurcation of Two Kinds of Three-Dimensional Fractional Lotka-Volterra Systems," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-8, March.
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    Cited by:

    1. Xie, Jiaquan & Zhao, Fuqiang & He, Dongping & Shi, Wei, 2022. "Bifurcation and resonance of fractional cubic nonlinear system," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).

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