ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

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Doroshenko V. M. Strange nonchaotic attractor of Hunt and Ott type in a system with ring geometry. Izvestiya VUZ. Applied Nonlinear Dynamics, 2016, vol. 24, iss. 1, pp. 16-30. DOI: 10.18500/0869-6632-2016-24-1-16-30

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Language: 
Russian
Heading: 
Applied Problems of Nonlinear Oscillation and Wave Theory
Article type: 
Article
UDC: 
517.9
DOI: 
10.18500/0869-6632-2016-24-1-16-30

Strange nonchaotic attractor of Hunt and Ott type in a system with ring geometry

Autors: 
Doroshenko Valentina Mihajlovna, 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).

Key words: 
Strange nonchaotic attractor
Hunt-Ott map
robustness
fractal structure
singular continuous spectrum
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Received: 
26.02.2016
Accepted: 
28.02.2016
Published: 
28.02.2016
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