Geodesic
The Influence of Delayed Feedback Control on Stabilization of Periodic Orbits
Modelirovanie i analiz informacionnyh sistem, Tome 21 (2014) no. 1, pp. 53-65

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{MAIS_2014_21_1_a3,
     author = {V. G. Bogaevskaya and I. S. Kashchenko},
     title = {The {Influence} of {Delayed} {Feedback} {Control} on {Stabilization} of {Periodic} {Orbits}},
     journal = {Modelirovanie i analiz informacionnyh sistem},
     pages = {53--65},
     publisher = {mathdoc},
     volume = {21},
     number = {1},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MAIS_2014_21_1_a3/}
}
TY  - JOUR
AU  - V. G. Bogaevskaya
AU  - I. S. Kashchenko
TI  - The Influence of Delayed Feedback Control on Stabilization of Periodic Orbits
JO  - Modelirovanie i analiz informacionnyh sistem
PY  - 2014
SP  - 53
EP  - 65
VL  - 21
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MAIS_2014_21_1_a3/
LA  - ru
ID  - MAIS_2014_21_1_a3
ER  - 
%0 Journal Article
%A V. G. Bogaevskaya
%A I. S. Kashchenko
%T The Influence of Delayed Feedback Control on Stabilization of Periodic Orbits
%J Modelirovanie i analiz informacionnyh sistem
%D 2014
%P 53-65
%V 21
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MAIS_2014_21_1_a3/
%G ru
%F MAIS_2014_21_1_a3
V. G. Bogaevskaya; I. S. Kashchenko. The Influence of Delayed Feedback Control on Stabilization of Periodic Orbits. Modelirovanie i analiz informacionnyh sistem, Tome 21 (2014) no. 1, pp. 53-65. http://geodesic.mathdoc.fr/item/MAIS_2014_21_1_a3/