Publication result detail

Optimal piecewise-linear approximation of the quadratic chaotic dynamics

PETRŽELA, J.

Original Title

Optimal piecewise-linear approximation of the quadratic chaotic dynamics

English Title

Optimal piecewise-linear approximation of the quadratic chaotic dynamics

Type

Peer-reviewed article not indexed in WoS or Scopus

Original Abstract

This paper shows the influence of piecewise-linear approximation on the global dynamics associated with autonomous third-order dynamical systems with the quadratic vector fields. The novel method for optimal nonlinear function approximation preserving the system behavior is proposed and experimentally verified. This approach is based on the calculation of the state attractor metric dimension inside a stochastic optimization routine. The approximated systems are compared to the original by means of the numerical integration. Real electronic circuits representing individual dynamical systems are derived using classical as well as integrator-based synthesis and verified by time-domain analysis in Orcad Pspice simulator. The universality of the proposed method is briefly discussed, especially from the viewpoint of the higher-order dynamical systems. Future topics and perspectives are also provided.

English abstract

This paper shows the influence of piecewise-linear approximation on the global dynamics associated with autonomous third-order dynamical systems with the quadratic vector fields. The novel method for optimal nonlinear function approximation preserving the system behavior is proposed and experimentally verified. This approach is based on the calculation of the state attractor metric dimension inside a stochastic optimization routine. The approximated systems are compared to the original by means of the numerical integration. Real electronic circuits representing individual dynamical systems are derived using classical as well as integrator-based synthesis and verified by time-domain analysis in Orcad Pspice simulator. The universality of the proposed method is briefly discussed, especially from the viewpoint of the higher-order dynamical systems. Future topics and perspectives are also provided.

Keywords

Chaotic dynamics, Lyapunov exponents, piecewise-linear approximation, stochastic optimization

Key words in English

Chaotic dynamics, Lyapunov exponents, piecewise-linear approximation, stochastic optimization

Authors

PETRŽELA, J.

RIV year

2013

Released

02.04.2012

ISBN

1210-2512

Periodical

Radioengineering

Volume

21

Number

1

State

Czech Republic

Pages from

20

Pages to

28

Pages count

9

BibTex

@article{BUT91822,
  author="Jiří {Petržela}",
  title="Optimal piecewise-linear approximation of the quadratic chaotic dynamics",
  journal="Radioengineering",
  year="2012",
  volume="21",
  number="1",
  pages="20--28",
  issn="1210-2512"
}