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Zero-Hopf bifurcation in the generalized Michelson system

Author

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  • Llibre, Jaume
  • Makhlouf, Amar

Abstract

We provide sufficient conditions for the existence of two periodic solutions bifurcating from a zero–Hopf equilibrium for the differential system x˙=y,y˙=z,z˙=a+by+cz−x2/2,where a, b and c are real arbitrary parameters. The regular perturbation of this differential system provides the normal form of the so–called triple–zero bifurcation.

Suggested Citation

  • Llibre, Jaume & Makhlouf, Amar, 2016. "Zero-Hopf bifurcation in the generalized Michelson system," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 228-231.
    • Handle: RePEc:eee:chsofr:v:89:y:2016:i:c:p:228-231
    DOI: 10.1016/j.chaos.2015.11.013
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    Cited by:

    1. Cang, Shijian & Wang, Luo & Zhang, Yapeng & Wang, Zenghui & Chen, Zengqiang, 2022. "Bifurcation and chaos in a smooth 3D dynamical system extended from Nosé-Hoover oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    2. Artés, Joan Carles & Llibre, Jaume & Valls, Claudià, 2018. "Dynamics of the Higgins–Selkov and Selkov systems," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 145-150.
    3. Chen, Xitong & Bao, Jianghong & Yu, Huanyu, 2021. "New insights into the extended Malkus-Robbins dynamo," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).

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