Dependence of hidden attractors on non-linearity and Hamilton energy in a class of chaotic system

Ge Zhang; Chunni Wang; Ahmed Alsaedi; Jun Ma; Guodong Ren

Kybernetika (2018)

  • Volume: 54, Issue: 4, page 648-663
  • ISSN: 0023-5954

Abstract

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Non-linearity is essential for occurrence of chaos in dynamical system. The size of phase space and formation of attractors are much dependent on the setting of nonlinear function and parameters. In this paper, a three-variable dynamical system is controlled by different nonlinear function thus a class of chaotic system is presented, the Hamilton function is calculated to find the statistical dynamical property of the improved dynamical systems composed of hidden attractors. The standard dynamical analysis is confirmed in numerical studies, and the dependence of attractors and Hamilton energy on non-linearity selection is discussed. It is found that lower average Hamilton energy can be detected when intensity of nonlinear function is enhanced. It indicates that non-linearity can decrease the energy cost triggering for dynamical behaviors.

How to cite

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Zhang, Ge, et al. "Dependence of hidden attractors on non-linearity and Hamilton energy in a class of chaotic system." Kybernetika 54.4 (2018): 648-663. <http://eudml.org/doc/294322>.

@article{Zhang2018,
abstract = {Non-linearity is essential for occurrence of chaos in dynamical system. The size of phase space and formation of attractors are much dependent on the setting of nonlinear function and parameters. In this paper, a three-variable dynamical system is controlled by different nonlinear function thus a class of chaotic system is presented, the Hamilton function is calculated to find the statistical dynamical property of the improved dynamical systems composed of hidden attractors. The standard dynamical analysis is confirmed in numerical studies, and the dependence of attractors and Hamilton energy on non-linearity selection is discussed. It is found that lower average Hamilton energy can be detected when intensity of nonlinear function is enhanced. It indicates that non-linearity can decrease the energy cost triggering for dynamical behaviors.},
author = {Zhang, Ge, Wang, Chunni, Alsaedi, Ahmed, Ma, Jun, Ren, Guodong},
journal = {Kybernetika},
keywords = {Helmholtz theorem; chaos; hidden attractor; bifurcation; Hamilton energy},
language = {eng},
number = {4},
pages = {648-663},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Dependence of hidden attractors on non-linearity and Hamilton energy in a class of chaotic system},
url = {http://eudml.org/doc/294322},
volume = {54},
year = {2018},
}

TY - JOUR
AU - Zhang, Ge
AU - Wang, Chunni
AU - Alsaedi, Ahmed
AU - Ma, Jun
AU - Ren, Guodong
TI - Dependence of hidden attractors on non-linearity and Hamilton energy in a class of chaotic system
JO - Kybernetika
PY - 2018
PB - Institute of Information Theory and Automation AS CR
VL - 54
IS - 4
SP - 648
EP - 663
AB - Non-linearity is essential for occurrence of chaos in dynamical system. The size of phase space and formation of attractors are much dependent on the setting of nonlinear function and parameters. In this paper, a three-variable dynamical system is controlled by different nonlinear function thus a class of chaotic system is presented, the Hamilton function is calculated to find the statistical dynamical property of the improved dynamical systems composed of hidden attractors. The standard dynamical analysis is confirmed in numerical studies, and the dependence of attractors and Hamilton energy on non-linearity selection is discussed. It is found that lower average Hamilton energy can be detected when intensity of nonlinear function is enhanced. It indicates that non-linearity can decrease the energy cost triggering for dynamical behaviors.
LA - eng
KW - Helmholtz theorem; chaos; hidden attractor; bifurcation; Hamilton energy
UR - http://eudml.org/doc/294322
ER -

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