Izvestiya of Saratov University.

Physics

ISSN 1817-3020 (Print)
ISSN 2542-193X (Online)

For citation:

Anishchenko V. S., Astakhov S. V., Boev Y. I., Biryukova N. I., Strelkova G. I. Statistics of Poincare Recurrence with Considering Effect of Fluctuations. Izvestiya of Saratov University. Physics , 2013, vol. 13, iss. 2, pp. 5-15. DOI: 10.18500/1817-3020-2013-13-2-5-15

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
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Language: 
Russian
Heading: 
Physics
UDC: 
537.86
DOI: 
10.18500/1817-3020-2013-13-2-5-15

Statistics of Poincare Recurrence with Considering Effect of Fluctuations

Autors: 
Anishchenko Vadim Semenovich, Saratov State University
Astakhov Sergey Vladimirovich, Lomonosov Moscow State University
Boev Yaroslav Igorevich, Saratov State University
Biryukova Nadezhda Igorevna, Saratov State University
Strelkova Galina Ivanovna, Saratov State University
Abstract: 

The basic statistical characteristics of Poincare recurrence are obtained numerically for the logistic map in a chaotic regime. The mean values, variation and recurrence distribution density are calculated and their dependence on a return size is analysed. Afraimovich–Pesin dimension values are obtained. It is verified that the Afraimovich–Pesin dimension corresponds to the Lyapunov exponent. the peculiarities of the influence of noise on the recurrence statistics are studied in local and global approaches. It is shown that the obtained numerical data fully conform to the theoretical results. It is demonstrated that the Poincare recurrence theory can be applied to diagnose.

Key words: 
Poincare recurrence
fractal dimension
topological entropy
Afraimovich–Pesin dimension
stochastic resonance
synchronization
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