SYSTEM OF THREE NONAUTONOMOUS OSCILLATORS WITH HYPERBOLIC CHAOS Part I The model with dynamics on attractor governed by Arnold’s cat map on torus
Cite this article as:
Arzhanukhina D. S., Kuznetsov S. P. SYSTEM OF THREE NONAUTONOMOUS OSCILLATORS WITH HYPERBOLIC CHAOS Part I The model with dynamics on attractor governed by Arnold’s cat map on torus. Izvestiya VUZ. Applied Nonlinear Dynamics, 2012, vol. 20, iss. 6, pp. 56-66. DOI: https://doi.org/10.18500/0869-6632-2012-20-6-56-66
In this paper a system of three coupled nonautonomous selfoscillatory elements is studied, in which the behavior of oscillators phases on a period of the coefficients variation in the equations corresponds to the Anosov map demonstrating chaotic dynamics. Results of numerical studies allow us to conclude that the attractor of the Poincare map can be viewed as an object roughly represented by a twodimensional torus embedded in the sixdimensional phase space of the Poincare map, on which the dynamics is the hyperbolic chaos intrinsic to Anosov’s systems.
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BibTeX
author = {D. S. Arzhanukhina and Sergey P. Kuznetsov},
title = {SYSTEM OF THREE NONAUTONOMOUS OSCILLATORS WITH HYPERBOLIC CHAOS Part I The model with dynamics on attractor governed by Arnold’s cat map on torus},
year = {2012},
journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
volume = {20},number = {6},
url = {https://old-andjournal.sgu.ru/en/articles/system-of-three-nonautonomous-oscillators-with-hyperbolic-chaos-part-i-the-model-with},
address = {Саратов},
language = {russian},
doi = {10.18500/0869-6632-2012-20-6-56-66},pages = {56--66},issn = {0869-6632},
keywords = {Attractor,hyperbolic chaos,Anosov map,Arnold’s cat map,Fibonacci map.},
abstract = {In this paper a system of three coupled nonautonomous selfoscillatory elements is studied, in which the behavior of oscillators phases on a period of the coefficients variation in the equations corresponds to the Anosov map demonstrating chaotic dynamics. Results of numerical studies allow us to conclude that the attractor of the Poincare map can be viewed as an object roughly represented by a twodimensional torus embedded in the sixdimensional phase space of the Poincare map, on which the dynamics is the hyperbolic chaos intrinsic to Anosov’s systems. }}