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 Model. Anal. Inform. Sist., 2014, Volume 21, Number 1, Pages 53–65 (Mi mais359)

The Influence of Delayed Feedback Control on Stabilization of Periodic Orbits

V. G. Bogaevskaya, I. S. Kashchenko

P. G. Demidov Yaroslavl State University, Sovetskaya str., 14, Yaroslavl, 150000, Russia

Abstract: In this paper we solve problems of stabilization of unstable cycle by the delay feedback. We study a model equation with qubic nonlinearity. In this case only one multiplicator is located outside a unit circle. Delay time is proportional to the cycle period. The $D$-partition of the parameter plane is obtained. The main result is analytically found conditions for parameters of delay control such that the initial cycle is stable. Also, we have found necessary and sufficient conditions of solvability of the stabilization problem. As a consequence, the problem of stablity of the Stuart–Landau equation periodic solution is completely solved.

Keywords: Stuart–Landau equation, delay control, cycle stabilization, multiplicators.

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UDC: 517.9

Citation: V. G. Bogaevskaya, I. S. Kashchenko, “The Influence of Delayed Feedback Control on Stabilization of Periodic Orbits”, Model. Anal. Inform. Sist., 21:1 (2014), 53–65

Citation in format AMSBIB
\Bibitem{BogKas14}
\by V.~G.~Bogaevskaya, I.~S.~Kashchenko
\paper The Influence of Delayed Feedback Control on Stabilization of Periodic Orbits
\jour Model. Anal. Inform. Sist.
\yr 2014
\vol 21
\issue 1
\pages 53--65
\mathnet{http://mi.mathnet.ru/mais359}