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Izvestiya VUZ. Applied Nonlinear Dynamics, 2016, Volume 24, Issue 1, Pages 16–30
(Mi ivp174)
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APPLIED PROBLEMS OF NONLINEAR OSCILLATION AND WAVE THEORY
Strange nonchaotic attractor of Hunt and Ott type in a system with ring geometry
V. M. Doroshenko Saratov State University
Abstract:
The physical realizable system of ring structure, with a fixed irrational ratio of basic frequencies of external driving (the golden mean) manifests a strange nonchaotic attractor (SNA), similar to the attractor in the abstract map on a torus proposed and analyzed earlier by Hunt and Ott as an example of robust SNA. Simulation of the dynamics is provided basing on the numerical integration of the corresponding non-autonomous system of differential equations with quasi-periodic coefficients. It has been demonstrated that in terms of appropriately chosen phase variables the dynamics on the characteristic period is consistent with the topology of the mapping of Hunt and Ott. It has been shown that the birth of SNA corresponds to the criterion of Pikovsky and Feudel. Numerical calculations show that the Fourier spectra in sustained mode is of intermediate class between the continuous and discrete spectra (the singular continuous spectrum).
Keywords:
Strange nonchaotic attractor, Hunt–Ott map, robustness, fractal structure, singular continuous spectrum.
Received: 26.02.2016
Citation:
V. M. Doroshenko, “Strange nonchaotic attractor of Hunt and Ott type in a system with ring geometry”, Izvestiya VUZ. Applied Nonlinear Dynamics, 24:1 (2016), 16–30
Linking options:
https://www.mathnet.ru/eng/ivp174 https://www.mathnet.ru/eng/ivp/v24/i1/p16
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Abstract page: | 63 | Full-text PDF : | 11 |
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