ATTRACTOR OF SMALE–WILLIAMS TYPE IN A RING SYSTEM WITH PERIODIC FREQUENCY MODULATION

Cite this article as:

Kruglov V. P. ATTRACTOR OF SMALE–WILLIAMS TYPE IN A RING SYSTEM WITH PERIODIC FREQUENCY MODULATION. Izvestiya VUZ. Applied Nonlinear Dynamics, 2012, vol. 20, iss. 1, pp. 124-128. DOI: https://doi.org/10.18500/0869-6632-2012-20-1-124-128

A scheme of circular nonautonomous system is introduced, which is supposed to generate hyperbolic chaos. Its operation is based on doubling of phase on complete cycle of the signal transmission. This is a criterion for the Smale–Williams attractor to exist. The performance is realized due to smooth periodic variation of natural frequency in one of the two oscillatory subsystems, which compose the ring, from reference value to the doubled one.

Authors: 
Kruglov V. P., Saratov State University, ul. Astrakhanskaya, 83, Saratov, 410012, Russia , kruglovyacheslav@gmail.com
Key words: 
hyperbolic chaos, Smale–Williams attractor, structural stability.
DOI: 
10.18500/0869-6632-2012-20-1-124-128
Literature

1. Kuznetsov S.P. Hyperbolic Chaos: A Physicist’s View. Higher Education Press: Beijing and Springer-Verlag, Berlin, Heidelberg, 2012. 336 p.

2. Кузнецов С.П. Динамический хаос и однородно гиперболические аттракторы: от математики к физике // Успехи физических наук. 2011. T. 181, No 2. C. 121.

3. Kuznetsov S.P. Example of a physical system with a hyperbolic attractor of the Smale–Williams type // Phys. Rev. Lett. 2005. Vol. 95. 144101.

4. Кузнецов А.П., Кузнецов С.П., Пиковский А.С., Тюрюкина Л.В. Хаотическая динамика в системах связанных неавтономных осцилляторов с резонансным и нерезонансным механизмом передачи возбуждения // Известия вузов. Прикладная нелинейная динамика. 2007. Т. 15, No 6. С. 75.

5. Кузнецов С.П. Динамический хаос. М.: Физматлит, 2006. 290 c.

Heading: 
Bifurcations in Dynamical Systems
Status: 
одобрено к публикации
Short Text (PDF): 
a2012no1p124.pdf

BibTeX

@article{Круглов-IzvVUZ_AND-20-1-124,
author = {V. P. Kruglov},
title = {ATTRACTOR OF SMALE–WILLIAMS TYPE IN A RING SYSTEM WITH PERIODIC FREQUENCY MODULATION},
year = {2012},
journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
volume = {20},number = {1},
url = {https://old-andjournal.sgu.ru/en/articles/attractor-of-smale-williams-type-in-ring-system-with-periodic-frequency-modulation},
address = {Саратов},
language = {russian},
doi = {10.18500/0869-6632-2012-20-1-124-128},pages = {124--128},issn = {0869-6632},
keywords = {hyperbolic chaos,Smale–Williams attractor,structural stability.},
abstract = {A scheme of circular nonautonomous system is introduced, which is supposed to generate hyperbolic chaos. Its operation is based on doubling of phase on complete cycle of the signal transmission. This is a criterion for the Smale–Williams attractor to exist. The performance is realized due to smooth periodic variation of natural frequency in one of the two oscillatory subsystems, which compose the ring, from reference value to the doubled one. }}