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

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Kuznetsov S. P. Hyperbolic strange attractors of physically realizable systems. Izvestiya VUZ. Applied Nonlinear Dynamics, 2009, vol. 17, iss. 4, pp. 5-34. DOI: 10.18500/0869-6632-2009-17-4-5-34

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Language: 
Russian
Heading: 
Review of Actual Problems of Nonlinear Dynamics
Article type: 
Review
UDC: 
517.9
DOI: 
10.18500/0869-6632-2009-17-4-5-34

Hyperbolic strange attractors of physically realizable systems

Autors: 
Kuznetsov Sergey Petrovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Abstract: 

A review of studies aimed on revealing or constructing physical systems with hyperbolic strange attractors, like Plykin attractor and Smale–Williams solenoid, is presented. Examples of iterated maps, differential equations, and simple electronic devices with chaotic dynamics associated with such attractors are presented and discussed. A general principle is considered and illustrated basing on manipulation of phases in alternately excited oscillators and time-delay systems. Alternative approaches are reviewed outlined in literature, as well as the prospects of further researches.

Key words: 
Attractor
dynamical system
Poincare map
Smale–Williams solenoid
Plykin attractor
hyperbolic chaos
oscillator
chaos generator
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Received: 
29.06.2009
Accepted: 
29.06.2009
Published: 
30.10.2009
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