Periodic parametric perturbation control for a 3D autonomous chaotic system and its dynamics at infinity

Zhen Wang; Wei Sun; Zhouchao Wei; Shanwen Zhang

Kybernetika (2017)

  • Volume: 53, Issue: 2, page 354-369
  • ISSN: 0023-5954

Abstract

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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.

How to cite

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Wang, Zhen, et al. "Periodic parametric perturbation control for a 3D autonomous chaotic system and its dynamics at infinity." Kybernetika 53.2 (2017): 354-369. <http://eudml.org/doc/288189>.

@article{Wang2017,
abstract = {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.},
author = {Wang, Zhen, Sun, Wei, Wei, Zhouchao, Zhang, Shanwen},
journal = {Kybernetika},
keywords = {Hamiltonian system; Melnikov's methods; homoclinic orbits; periodic orbits; periodic parametric perturbation; dynamics at infinity},
language = {eng},
number = {2},
pages = {354-369},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Periodic parametric perturbation control for a 3D autonomous chaotic system and its dynamics at infinity},
url = {http://eudml.org/doc/288189},
volume = {53},
year = {2017},
}

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
PB - Institute of Information Theory and Automation AS CR
VL - 53
IS - 2
SP - 354
EP - 369
AB - 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.
LA - eng
KW - Hamiltonian system; Melnikov's methods; homoclinic orbits; periodic orbits; periodic parametric perturbation; dynamics at infinity
UR - http://eudml.org/doc/288189
ER -

References

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