Indecomposable continua in dynamical systems with noise: Fluid flow past an array of cylinders

Miguel A. F. Sanjuan, Judy Kennedy, Celso Grebogi, James A. Yorke

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34 Citations (Scopus)

Abstract

Standard dynamical systems theory is based on the study of invariant sets. However, when noise is added, there are no bounded invariant sets. Our goal is then to study the fractal structure that exists even with noise, The problem we investigate is fluid flow past an array of cylinders. We study a parameter range for which there is a periodic oscillation of the fluid, represented by vortices being shed past each cylinder. Since the motion is periodic in time, we can study a time-1 Poincare map. Then we add a small amount of noise, so that on each iteration the Poincare map is perturbed smoothly, but differently for each time cycle. Fix an x coordinate x(0) and an initial time t(0). We discuss when the set of initial points at a time t(0) whose trajectory (x(t),y(t)) is semibounded (i.e., x(t)>x(0) for all time) has a fractal structure called an indecomposable continuum. We believe that the indecomposable continuum will become a fundamental object in the study of dynamical systems with noise. (C) 1997 American Institute of Physics.

Original languageEnglish
Pages (from-to)125-138
Number of pages14
JournalChaos
Volume7
Issue number1
DOIs
Publication statusPublished - Mar 1997

Keywords

  • open hydrodynamical flows

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