Geodesic
About one approach to construction of chaotic chameleons systems
Čebyševskij sbornik, Tome 18 (2017) no. 4, pp. 128-139

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

Now it is well known that dynamical systems can be categorized into systems with self-excited attractors and systems with hidden attractors. A self-excited attractor has a basin of attraction that is associated with an unstable equilibrium, while a hidden attractor has a basin of attraction that does not intersect with small neighborhoods of any equilibrium points. Hidden attractors play the important role in engineering applications because they allow unexpected and potentially disastrous responses to perturbations in a structure like a bridge or an airplane wing. In addition, complex behaviors of chaotic systems have been applied in various areas from image watermarking, audio encryption scheme, asymmetric color pathological image encryption, chaotic masking communication to random number generator. Recently so-called chameleons systems have been found out by researchers. These systems were so are named for the reason, that they shows self-excited or hidden oscillations depending on the value of parameters entering into them. In the present work the simple algorithm of synthesizing of one-parametrical chameleons systems is offered. Evolution Lyapunov exponents and Kaplan-Yorke dimension of such systems at change of parameter is traced.
Keywords: self-excited attractor, hidden attractor, multistability, cycle, bifurcation, chameleon system, Lyapunov exponents, Kaplan–Yorke dimension. 
@article{CHEB_2017_18_4_a5,
     author = {I. M. Burkin},
     title = {About one approach to construction of chaotic chameleons systems},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {128--139},
     publisher = {mathdoc},
     volume = {18},
     number = {4},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2017_18_4_a5/}
}
TY  - JOUR
AU  - I. M. Burkin
TI  - About one approach to construction of chaotic chameleons systems
JO  - Čebyševskij sbornik
PY  - 2017
SP  - 128
EP  - 139
VL  - 18
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CHEB_2017_18_4_a5/
LA  - ru
ID  - CHEB_2017_18_4_a5
ER  - 
%0 Journal Article
%A I. M. Burkin
%T About one approach to construction of chaotic chameleons systems
%J Čebyševskij sbornik
%D 2017
%P 128-139
%V 18
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CHEB_2017_18_4_a5/
%G ru
%F CHEB_2017_18_4_a5
I. M. Burkin. About one approach to construction of chaotic chameleons systems. Čebyševskij sbornik, Tome 18 (2017) no. 4, pp. 128-139. http://geodesic.mathdoc.fr/item/CHEB_2017_18_4_a5/