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

  • Na Li
  • Junjie WeiEmail author
Original Paper


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.


Electro-optical oscillator Delayed bandpass feedback Bifurcation analysis Normal form 



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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Conflict of interest

The authors declare that they have no conflict of interest.

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Informed consent was obtained from all individual participants included in the study.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of MathematicsHarbin Institute of Technology at WeihaiWeihaiPeople’s Republic of China
  2. 2.School of Mathematics and Big DataFoshan UniversityFoshanPeople’s Republic of China

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