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Bifurcation analysis in a nonlinear electro-optical oscillator with delayed bandpass feedback

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Abstract

The dynamics of a nonlinear electro-optical oscillator with delayed bandpass feedback is investigated. By analyzing the distribution of the eigenvalues, the existence and stability of Hopf bifurcations are obtained. Particularly, the stability switches are found as the delay varies, where the time delay is regarded as bifurcation parameter. And then, by applying the normal form method and center manifold theory of functional differential equations, an algorithm for determining the sense of the Hopf bifurcations and stability of the bifurcating periodic solutions is derived. For illustrating the theoretical results, some numerical simulations are performed.

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Acknowledgements

The authors are grateful to the anonymous referees for their helpful comments and valuable suggestions which have improved the presentation of the paper.

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Authors and Affiliations

  1. Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai, 264209, Shandong, People’s Republic of China

    Na Li & Junjie Wei

  2. School of Mathematics and Big Data, Foshan University, Foshan, 528000, Guangdong, People’s Republic of China

    Junjie Wei

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  1. Na Li
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  2. Junjie Wei
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Correspondence to Junjie Wei.

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This research is partially supported by National Natural Science Foundation of China (No.11771109).

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Li, N., Wei, J. Bifurcation analysis in a nonlinear electro-optical oscillator with delayed bandpass feedback. Nonlinear Dyn 96, 483–496 (2019). https://doi.org/10.1007/s11071-019-04801-4

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