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We investigate the normal form of a subcritical Hopf bifurcation subjected to time-delayed feedback control. Bifurcation diagrams which cover time-dependent states as well are obtained by analytical means. The computations show that unstable limit cycles with an odd number of positive Floquet exponents can be stabilized by time-delayed feedback control, contrary to incorrect claims in the literature. The model system constitutes one of the few examples where a nonlinear time delay system can be treated entirely by analytical means.
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Just et al. (2007) studied this question.
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