Abstract
The previous section showed that the alleged odd-number theorem is not valid for autonomous systems and that in fact an odd-number orbit born in a subcritical Hopf bifurcation can be stabilized by time-delayed feedback control. Although this is a very generic example, the question arises whether this situation close to the Hopf bifurcation is special or if odd-number orbits born from other bifurcations can be stabilized, too.
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References
B. Fiedler, S. Yanchuk, V. Flunkert, P. Hövel, H.J. Wünsche, E. Schöll, Delay stabilization of rotating waves near fold bifurcation and application to all-optical control of a semiconductor laser. Phys. Rev. E 77, 066207 (2008)
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© 2011 Springer-Verlag Berlin Heidelberg
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Flunkert, V. (2011). Odd-Number Orbits Close to a Fold Bifurcation. In: Delay-Coupled Complex Systems. Springer Theses. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20250-6_4
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DOI: https://doi.org/10.1007/978-3-642-20250-6_4
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