Poincaré Recurrences in a Nonautonomous Chaotic Map-Reference-Cited by-同舟云学术

Poincaré Recurrences in a Nonautonomous Chaotic Map

Published:2014-08 Issue:08 Volume:24 Page:1440016
ISSN:0218-1274
Container-title:International Journal of Bifurcation and Chaos
language:en
Short-container-title:Int. J. Bifurcation Chaos

Author:

Boev Yaroslav¹,Semenova Nadezhda¹,Strelkova Galina¹,Anishchenko Vadim¹

Affiliation:

1. Department of Physics, Saratov State University, 83 Astrakhanskaya Str., Saratov 410012, Russia

Abstract

The statistics of Poincaré recurrences is studied numerically in a one-dimensional cubic map in the presence of harmonic and noisy excitations. It is shown that the distribution density of Poincaré recurrences is periodically modulated by the harmonic force. It is established that the relationship between the Afraimovich–Pesin dimension and Lyapunov exponents is violated in the nonautonomous system.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modelling and Simulation,Engineering (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218127414400161

Reference19 articles.

1. V. S. Afraimovich and L. P. Shilnikov, Nonlinear Dynamics and Turbulence, eds. G. I. Barenblatt and D. D. Joseph (Pitman, NY, 1983) pp. 1–28.

2. Pesin’s dimension for Poincaré recurrences

3. FRACTAL DIMENSION FOR POINCARÉ RECURRENCES AS AN INDICATOR OF SYNCHRONIZED CHAOTIC REGIMES

4. Effects of strong noise on attractors of dynamical systems

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