Hidden Strange Nonchaotic Attractors

Marius-F. Danca and Nikolay Kuznetsov
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Marius-F. Danca: Romanian Romanian Institute of Science and Technology, 400487 Cluj-Napoca, Romania
Nikolay Kuznetsov: Department of Applied Cybernetics, Saint-Petersburg State University, Peterhof, 198504 Saint-Petersburg, Russia

Mathematics, 2021, vol. 9, issue 6, 1-19

Abstract: 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: hidden chaotic attractor; self-excited attractor; strange nonchaotic attractor; Rabinovich–Fabrikant system (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

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