6533b7d3fe1ef96bd126025b

RESEARCH PRODUCT

Hidden Strange Nonchaotic Attractors

Marius-f. DancaNikolay Kuznetsov

subject

Mathematics::Dynamical SystemsGeneral MathematicsChaoticattraktoritLyapunov exponenthidden chaotic attractor01 natural sciencesStrange nonchaotic attractor010305 fluids & plasmassymbols.namesakeFractalRabinovich–Fabrikant system0103 physical sciencesAttractorComputer Science (miscellaneous)Statistical physicsdynaamiset systeemitRecurrence plot010301 acousticsEngineering (miscellaneous)BifurcationPhysicskaaosteorialcsh:Mathematicslcsh:QA1-939strange nonchaotic attractorself-excited attractorNonlinear Sciences::Chaotic DynamicsQuasiperiodic functionsymbolsfraktaalit

description

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.

yearjournalcountryeditionlanguage
2021-03-01Mathematics
https://doi.org/10.3390/math9060652