Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Refuting the odd number limitation of time-delayed feedback control   We refute an often invoked theorem which claims that a periodic orbit with an
odd number of real Floquet multipliers greater than unity can never be
stabilized by time-delayed feedback control in the form proposed by Pyragas.
Using a generic normal form, we demonstrate that the unstable periodic orbit
generated by a subcritical Hopf bifurcation, which has a single real unstable
Floquet multiplier, can in fact be stabilized. We derive explicit analytical
conditions for the control matrix in terms of the amplitude and the phase of
the feedback control gain, and present a numerical example. Our results are of
relevance for a wide range of systems in physics, chemistry, technology,and
life sciences, where subcritical Hopf bifurcations occur.

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The categories of this paper are: mtrl-th
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The categories of this paper are: q-bio
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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc
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The categories of this paper are: q-alg
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The categories of this paper are: chem-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: patt-sol
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The categories of this paper are: q-fin
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The categories of this paper are: physics
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The categories of this paper are: math
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-th