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