Hidden attractors localization in Chua circuit via the describing function method

Research output

6 Citations (Scopus)

Abstract

In this paper the Chua circuit with five linear elements and saturation non-linearity is studied. Numerical localization of self-excited attractor in the Chua circuit model can be done by computation of trajectory with initial data in a vicinity of an unstable equilibrium. For a hidden attractor its basin of attraction does not overlap with a small vicinity of equilibria, so it is difficult to find the corresponding initial data for localization. This survey is devoted to the application of describing function method for localization of hidden periodic and chaotic attractors in the Chua model. We use a rigorous justification of the describing function method, based on the method of small parameter, to get the initial data for the visualization of the hidden attractors. A new configuration of hidden Chua attractors is presented.

Original languageEnglish
Pages (from-to)2651-2656
Number of pages6
JournalIFAC-PapersOnLine
Volume50
Issue number1
DOIs
Publication statusPublished - 1 Jul 2017

Fingerprint

Describing functions
Networks (circuits)
Visualization
Trajectories

Scopus subject areas

  • Control and Systems Engineering

Cite this

@article{9f1386b274494ecd907c82b0171f45e1,
title = "Hidden attractors localization in Chua circuit via the describing function method",
abstract = "In this paper the Chua circuit with five linear elements and saturation non-linearity is studied. Numerical localization of self-excited attractor in the Chua circuit model can be done by computation of trajectory with initial data in a vicinity of an unstable equilibrium. For a hidden attractor its basin of attraction does not overlap with a small vicinity of equilibria, so it is difficult to find the corresponding initial data for localization. This survey is devoted to the application of describing function method for localization of hidden periodic and chaotic attractors in the Chua model. We use a rigorous justification of the describing function method, based on the method of small parameter, to get the initial data for the visualization of the hidden attractors. A new configuration of hidden Chua attractors is presented.",
keywords = "Chua circuit, describing function method, hidden attractor, self-excited attractor",
author = "Kuznetsov, {N. V.} and Kuznetsova, {O. A.} and Leonov, {G. A.} and Mokaev, {T. N.} and Stankevich, {N. V.}",
year = "2017",
month = "7",
day = "1",
doi = "10.1016/j.ifacol.2017.08.470",
language = "English",
volume = "50",
pages = "2651--2656",
journal = "IFAC-PapersOnLine",
issn = "2405-8963",
publisher = "Elsevier",
number = "1",

}

TY - JOUR

T1 - Hidden attractors localization in Chua circuit via the describing function method

AU - Kuznetsov, N. V.

AU - Kuznetsova, O. A.

AU - Leonov, G. A.

AU - Mokaev, T. N.

AU - Stankevich, N. V.

PY - 2017/7/1

Y1 - 2017/7/1

N2 - In this paper the Chua circuit with five linear elements and saturation non-linearity is studied. Numerical localization of self-excited attractor in the Chua circuit model can be done by computation of trajectory with initial data in a vicinity of an unstable equilibrium. For a hidden attractor its basin of attraction does not overlap with a small vicinity of equilibria, so it is difficult to find the corresponding initial data for localization. This survey is devoted to the application of describing function method for localization of hidden periodic and chaotic attractors in the Chua model. We use a rigorous justification of the describing function method, based on the method of small parameter, to get the initial data for the visualization of the hidden attractors. A new configuration of hidden Chua attractors is presented.

AB - In this paper the Chua circuit with five linear elements and saturation non-linearity is studied. Numerical localization of self-excited attractor in the Chua circuit model can be done by computation of trajectory with initial data in a vicinity of an unstable equilibrium. For a hidden attractor its basin of attraction does not overlap with a small vicinity of equilibria, so it is difficult to find the corresponding initial data for localization. This survey is devoted to the application of describing function method for localization of hidden periodic and chaotic attractors in the Chua model. We use a rigorous justification of the describing function method, based on the method of small parameter, to get the initial data for the visualization of the hidden attractors. A new configuration of hidden Chua attractors is presented.

KW - Chua circuit

KW - describing function method

KW - hidden attractor

KW - self-excited attractor

UR - http://www.scopus.com/inward/record.url?scp=85031803225&partnerID=8YFLogxK

U2 - 10.1016/j.ifacol.2017.08.470

DO - 10.1016/j.ifacol.2017.08.470

M3 - Article

AN - SCOPUS:85031803225

VL - 50

SP - 2651

EP - 2656

JO - IFAC-PapersOnLine

JF - IFAC-PapersOnLine

SN - 2405-8963

IS - 1

ER -