Geodesic
Periodic parametric perturbation control for a 3D autonomous chaotic system and its dynamics at infinity
Kybernetika, Tome 53 (2017) no. 2, pp. 354-369.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

Periodic parametric perturbation control and dynamics at infinity for a 3D autonomous quadratic chaotic system are studied in this paper. Using the Melnikov's method, the existence of homoclinic orbits, oscillating periodic orbits and rotating periodic orbits are discussed after transferring the 3D autonomous chaotic system to a slowly varying oscillator. Moreover, the parameter bifurcation conditions of these orbits are obtained. In order to study the global structure, the dynamics at infinity of this system are analyzed through Poincaré compactification. The simulation results demonstrate feasibility of periodic parametric perturbation control technology and correctness of the theoretical results.
DOI : 10.14736/kyb-2017-2-0354
Classification : 34D20, 34H10, 34H20
Keywords: Hamiltonian system; Melnikov's methods; homoclinic orbits; periodic orbits; periodic parametric perturbation; dynamics at infinity 
@article{10_14736_kyb_2017_2_0354,
     author = {Wang, Zhen and Sun, Wei and Wei, Zhouchao and Zhang, Shanwen},
     title = {Periodic parametric perturbation control for a {3D} autonomous chaotic system and its dynamics at infinity},
     journal = {Kybernetika},
     pages = {354--369},
     publisher = {mathdoc},
     volume = {53},
     number = {2},
     year = {2017},
     doi = {10.14736/kyb-2017-2-0354},
     mrnumber = {3661356},
     zbl = {06770172},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.14736/kyb-2017-2-0354/}
}
TY  - JOUR
AU  - Wang, Zhen
AU  - Sun, Wei
AU  - Wei, Zhouchao
AU  - Zhang, Shanwen
TI  - Periodic parametric perturbation control for a 3D autonomous chaotic system and its dynamics at infinity
JO  - Kybernetika
PY  - 2017
SP  - 354
EP  - 369
VL  - 53
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.14736/kyb-2017-2-0354/
DO  - 10.14736/kyb-2017-2-0354
LA  - en
ID  - 10_14736_kyb_2017_2_0354
ER  - 
%0 Journal Article
%A Wang, Zhen
%A Sun, Wei
%A Wei, Zhouchao
%A Zhang, Shanwen
%T Periodic parametric perturbation control for a 3D autonomous chaotic system and its dynamics at infinity
%J Kybernetika
%D 2017
%P 354-369
%V 53
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.14736/kyb-2017-2-0354/
%R 10.14736/kyb-2017-2-0354
%G en
%F 10_14736_kyb_2017_2_0354
Wang, Zhen; Sun, Wei; Wei, Zhouchao; Zhang, Shanwen. Periodic parametric perturbation control for a 3D autonomous chaotic system and its dynamics at infinity. Kybernetika, Tome 53 (2017) no. 2, pp. 354-369. doi : 10.14736/kyb-2017-2-0354. http://geodesic.mathdoc.fr/articles/10.14736/kyb-2017-2-0354/

Cité par Sources :