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Hopf bifurcation and its control in a 3D autonomous system

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Abstract

The first section of this paper discusses the stability and Hopf bifurcation for a new dynamical system using stability theory, the center manifold as well as normal form theory. To verify the analytical results, numerical simulations are performed. The second section focuses on controlling the Hopf bifurcation with a robust controller capable of handling a wide range of parameter values. By fine tuning the control parameters, the controller ensures that Hopf bifurcation occurred at \(P_{0}\). Furthermore, we postpone the Hopf bifurcation at \(P_{+}\) by adjusting the control parameters.

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Acknowledgements

This research is financially supported by the National Science Foundation of China (Nos. 11772148, 11872201, 12172166).

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Authors and Affiliations

  1. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, Jiangsu, China

    Liangqiang Zhou & Albert Kabbah

  2. Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles(NUAA), MIIT, Nanjing, 210016, Jiangsu, China

    Liangqiang Zhou & Albert Kabbah

Authors
  1. Liangqiang Zhou
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  2. Albert Kabbah
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Correspondence to Liangqiang Zhou.

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Zhou, L., Kabbah, A. Hopf bifurcation and its control in a 3D autonomous system. Eur. Phys. J. Spec. Top. 231, 2115–2124 (2022). https://doi.org/10.1140/epjs/s11734-022-00488-8

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  • DOI: https://doi.org/10.1140/epjs/s11734-022-00488-8

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