Hidden Strange Nonchaotic Attractors
Danca, Marius-F., & Kuznetsov, N. (2021). Hidden Strange Nonchaotic Attractors. Mathematics, 9(6), Article 652. https://doi.org/10.3390/math9060652
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2021Copyright
© 2021 by the authors. Licensee MDPI, Basel, Switzerland
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.
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The work is supported by the Russian Science Foundation 19-41-02002 and St. Petersburg State University.License
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