Counting unstable periodic orbits in noisy chaotic systems: A scaling relation connecting experiment with theory

Chaos
Xing PeiYing-Cheng Lai

Abstract

The experimental detection of unstable periodic orbits in dynamical systems, especially those which yield short, noisy or nonstationary data sets, is a current topic of interest in many research areas. Unfortunately, for such data sets, only a few of the lowest order periods can be detected with quantifiable statistical accuracy. The primary observable is the number of encounters the general trajectory has with a particular orbit. Here we show that, in the limit of large period, this quantity scales exponentially with the period, and that this scaling is robust to dynamical noise. (c) 1998 American Institute of Physics.

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Citations

Jun 5, 2003·Chaos·R. GilmoreFrank Moss
Feb 6, 2017·Scientific Reports·Tongfeng WengPan Hui
Nov 23, 2000·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·M DhamalaE J Kostelich
Dec 2, 2000·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·W BraunM Huber
Nov 14, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Huanfei MaWei Lin
Dec 12, 2001·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·M DhamalaE J Kostelich

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