A1 Journal article (refereed)
Hidden Strange Nonchaotic Attractors (2021)

Danca, M.-F., & Kuznetsov, N. (2021). Hidden Strange Nonchaotic Attractors. Mathematics, 9(6), Article 652. https://doi.org/10.3390/math9060652

JYU authors or editors

Publication details

All authors or editors: Danca, Marius-F.; Kuznetsov, Nikolay

Journal or series: Mathematics

eISSN: 2227-7390

Publication year: 2021

Volume: 9

Issue number: 6

Article number: 652

Publisher: MDPI AG

Publication country: Switzerland

Publication language: English

DOI: https://doi.org/10.3390/math9060652

Publication open access: Openly available

Publication channel open access: Open Access channel

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/74821


In this paper, it is found numerically that the previously found hidden chaotic attractors of the Rabinovich–Fabrikant system actually present the characteristics of strange nonchaotic attractors. For a range of the bifurcation parameter, the hidden attractor is manifestly fractal with aperiodic dynamics, and even the finite-time largest Lyapunov exponent, a measure of trajectory separation with nearby initial conditions, is negative. To verify these characteristics numerically, the finite-time Lyapunov exponents, ‘0-1’ test, power spectra density, and recurrence plot are used. Beside the considered hidden strange nonchaotic attractor, a self-excited chaotic attractor and a quasiperiodic attractor of the Rabinovich–Fabrikant system are comparatively analyzed.

Keywords: dynamical systems; chaos theory; attractors; fractals

Free keywords: hidden chaotic attractor; self-excited attractor; strange nonchaotic attractor; Rabinovich–Fabrikant system

Contributing organizations

Ministry reporting: Yes

Reporting Year: 2021

Preliminary JUFO rating: 0

Last updated on 2021-20-09 at 15:32