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Graphical Structure of Attraction Basins of Hidden Chaotic Attractors : The Rabinovich-Fabrikant System. / Danca, Marius F.; Bourke, Paul; Kuznetsov, Nikolay.

In: International Journal of Bifurcation and Chaos, Vol. 29, No. 1, 1930001, 01.01.2019.

Research output: Contribution to journal › Article › peer-review

Harvard

Danca, MF, Bourke, P & Kuznetsov, N 2019, 'Graphical Structure of Attraction Basins of Hidden Chaotic Attractors: The Rabinovich-Fabrikant System', International Journal of Bifurcation and Chaos, vol. 29, no. 1, 1930001. https://doi.org/10.1142/S0218127419300015

APA

Danca, M. F., Bourke, P., & Kuznetsov, N. (2019). Graphical Structure of Attraction Basins of Hidden Chaotic Attractors: The Rabinovich-Fabrikant System. International Journal of Bifurcation and Chaos, 29(1), [1930001]. https://doi.org/10.1142/S0218127419300015

Vancouver

Danca MF, Bourke P, Kuznetsov N. Graphical Structure of Attraction Basins of Hidden Chaotic Attractors: The Rabinovich-Fabrikant System. International Journal of Bifurcation and Chaos. 2019 Jan 1;29(1). 1930001. https://doi.org/10.1142/S0218127419300015

Author

Danca, Marius F. ; Bourke, Paul ; Kuznetsov, Nikolay. / Graphical Structure of Attraction Basins of Hidden Chaotic Attractors : The Rabinovich-Fabrikant System. In: International Journal of Bifurcation and Chaos. 2019 ; Vol. 29, No. 1.

BibTeX

@article{8969bac17d72435ba14d959ef65e1dcf,
title = "Graphical Structure of Attraction Basins of Hidden Chaotic Attractors: The Rabinovich-Fabrikant System",
abstract = "The attraction basin of hidden attractors does not intersect with small neighborhoods of any equilibrium point. To the best of our knowledge this property has not been explored using realtime interactive three-dimensions graphics. Aided by advanced computer graphic analysis, in this paper, we explore this characteristic of a particular nonlinear system with very rich and unusual dynamics, the Rabinovich-Fabrikant system. It is shown that there exists a neighborhood of one of the unstable equilibria within which the initial conditions do not lead to the considered hidden chaotic attractor, but to one of the stable equilibria or are divergent. The trajectories starting from any neighborhood of the other unstable equilibria are attracted either by the stable equilibria, or are divergent.",
keywords = "Data visualisation, Hidden chaotic attractor, Rabinovich-Fabrikant system, AIZERMAN, LIMIT-CYCLES, ALGORITHMS, OSCILLATIONS, BIFURCATION, MULTISTABILITY",
author = "Danca, {Marius F.} and Paul Bourke and Nikolay Kuznetsov",
year = "2019",
month = jan,
day = "1",
doi = "10.1142/S0218127419300015",
language = "English",
volume = "29",
journal = "International Journal of Bifurcation and Chaos in Applied Sciences and Engineering",
issn = "0218-1274",
publisher = "WORLD SCIENTIFIC PUBL CO PTE LTD",
number = "1",

}

RIS

TY - JOUR

T1 - Graphical Structure of Attraction Basins of Hidden Chaotic Attractors

T2 - The Rabinovich-Fabrikant System

AU - Danca, Marius F.

AU - Bourke, Paul

AU - Kuznetsov, Nikolay

PY - 2019/1/1

Y1 - 2019/1/1

N2 - The attraction basin of hidden attractors does not intersect with small neighborhoods of any equilibrium point. To the best of our knowledge this property has not been explored using realtime interactive three-dimensions graphics. Aided by advanced computer graphic analysis, in this paper, we explore this characteristic of a particular nonlinear system with very rich and unusual dynamics, the Rabinovich-Fabrikant system. It is shown that there exists a neighborhood of one of the unstable equilibria within which the initial conditions do not lead to the considered hidden chaotic attractor, but to one of the stable equilibria or are divergent. The trajectories starting from any neighborhood of the other unstable equilibria are attracted either by the stable equilibria, or are divergent.

AB - The attraction basin of hidden attractors does not intersect with small neighborhoods of any equilibrium point. To the best of our knowledge this property has not been explored using realtime interactive three-dimensions graphics. Aided by advanced computer graphic analysis, in this paper, we explore this characteristic of a particular nonlinear system with very rich and unusual dynamics, the Rabinovich-Fabrikant system. It is shown that there exists a neighborhood of one of the unstable equilibria within which the initial conditions do not lead to the considered hidden chaotic attractor, but to one of the stable equilibria or are divergent. The trajectories starting from any neighborhood of the other unstable equilibria are attracted either by the stable equilibria, or are divergent.

KW - Data visualisation

KW - Hidden chaotic attractor

KW - Rabinovich-Fabrikant system

KW - AIZERMAN

KW - LIMIT-CYCLES

KW - ALGORITHMS

KW - OSCILLATIONS

KW - BIFURCATION

KW - MULTISTABILITY

UR - http://www.scopus.com/inward/record.url?scp=85061430754&partnerID=8YFLogxK

UR - http://www.mendeley.com/research/graphical-structure-attraction-basins-hidden-chaotic-attractors-rabinovichfabrikant-system

U2 - 10.1142/S0218127419300015

DO - 10.1142/S0218127419300015

M3 - Article

AN - SCOPUS:85061430754

VL - 29

JO - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

JF - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

SN - 0218-1274

IS - 1

M1 - 1930001

ER -

ID: 42960002