Geodesic
An approach to generating extremely multistable chaotic systems
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference "Geometric Methods in Control Theory and Mathematical Physics" dedicated to the 70th anniversary of S.L. Atanasyan, the 70th anniversary of I.S. Krasilshchik, the 70th anniversary of A.V. Samokhin, and the 80th anniversary of V.T. Fomenko. S.A. Esenin Ryazan State University, Ryazan, September 25–28, 2018. Part 1, Tome 168 (2019), pp. 15-25

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

In this paper, we propose new approaches to the construction of extremely multistable systems containing one-, two-, and three-dimensional lattices of identical hidden chaotic attractors possessing the same Lyapunov exponents. In particular, we prove that for multidimensional models of automatic control systems in the Lurie form, it is always possible to pass from interactive system to a cascade system; this substantially simplifies the procedure for constructing multidimensional lattices of identical chaotic attractors.
Keywords: dynamical system, extreme multistability, displacement of phase flow, Lyapunov exponent, Kaplan–Yorke dimension.
Mots-clés : chaos 
@article{INTO_2019_168_a2,
     author = {I. M. Burkin and O. I. Kuznetsova},
     title = {An approach to generating extremely multistable chaotic systems},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {15--25},
     publisher = {mathdoc},
     volume = {168},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2019_168_a2/}
}
TY  - JOUR
AU  - I. M. Burkin
AU  - O. I. Kuznetsova
TI  - An approach to generating extremely multistable chaotic systems
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2019
SP  - 15
EP  - 25
VL  - 168
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2019_168_a2/
LA  - ru
ID  - INTO_2019_168_a2
ER  - 
%0 Journal Article
%A I. M. Burkin
%A O. I. Kuznetsova
%T An approach to generating extremely multistable chaotic systems
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2019
%P 15-25
%V 168
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2019_168_a2/
%G ru
%F INTO_2019_168_a2
I. M. Burkin; O. I. Kuznetsova. An approach to generating extremely multistable chaotic systems. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference "Geometric Methods in Control Theory and Mathematical Physics" dedicated to the 70th anniversary of S.L. Atanasyan, the 70th anniversary of I.S. Krasilshchik, the 70th anniversary of A.V. Samokhin, and the 80th anniversary of V.T. Fomenko. S.A. Esenin Ryazan State University, Ryazan, September 25–28, 2018. Part 1, Tome 168 (2019), pp. 15-25. http://geodesic.mathdoc.fr/item/INTO_2019_168_a2/