Geodesic
Hidden oscillations in dynamical systems. 16 Hilbert's problem, Aizerman's and Kalman's conjectures, hidden attractors in Chua's circuits
Contemporary Mathematics. Fundamental Directions, Proceedings of the Sixth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2011). Part 1, Tome 45 (2012), pp. 105-121

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

The present survey is devoted to efficient methods for localization of hidden oscillations in dynamical systems. Their application to Hilbert's sixteenth problem for quadratic systems, Aizerman's problem, and Kalman's problem on absolute stability of control systems, and to the localization of chaotic hidden attractors (the basin of attraction of which does not contain neighborhoods of equilibria) is considered. The synthesis of the describing function method with the applied bifurcation theory and numerical methods for computing hidden oscillations is described. 
@article{CMFD_2012_45_a7,
     author = {G. A. Leonov and N. V. Kuznetsov},
     title = {Hidden oscillations in dynamical systems. 16 {Hilbert's} problem, {Aizerman's} and {Kalman's} conjectures, hidden attractors in {Chua's} circuits},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {105--121},
     publisher = {mathdoc},
     volume = {45},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2012_45_a7/}
}
TY  - JOUR
AU  - G. A. Leonov
AU  - N. V. Kuznetsov
TI  - Hidden oscillations in dynamical systems. 16 Hilbert's problem, Aizerman's and Kalman's conjectures, hidden attractors in Chua's circuits
JO  - Contemporary Mathematics. Fundamental Directions
PY  - 2012
SP  - 105
EP  - 121
VL  - 45
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMFD_2012_45_a7/
LA  - ru
ID  - CMFD_2012_45_a7
ER  - 
%0 Journal Article
%A G. A. Leonov
%A N. V. Kuznetsov
%T Hidden oscillations in dynamical systems. 16 Hilbert's problem, Aizerman's and Kalman's conjectures, hidden attractors in Chua's circuits
%J Contemporary Mathematics. Fundamental Directions
%D 2012
%P 105-121
%V 45
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMFD_2012_45_a7/
%G ru
%F CMFD_2012_45_a7
G. A. Leonov; N. V. Kuznetsov. Hidden oscillations in dynamical systems. 16 Hilbert's problem, Aizerman's and Kalman's conjectures, hidden attractors in Chua's circuits. Contemporary Mathematics. Fundamental Directions, Proceedings of the Sixth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2011). Part 1, Tome 45 (2012), pp. 105-121. http://geodesic.mathdoc.fr/item/CMFD_2012_45_a7/