Migration Towards Periodicity in Systems With Feedback
Wotherspoon, Timothy David
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Permalink
https://hdl.handle.net/2142/80624
Description
Title
Migration Towards Periodicity in Systems With Feedback
Author(s)
Wotherspoon, Timothy David
Issue Date
2009
Doctoral Committee Chair(s)
Karin Dahmen
Department of Study
Physics
Discipline
Physics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Physics, Theory
Language
eng
Abstract
We study adaptation to the edge of chaos in dynamical systems as caused by feedback mechanisms between the state variables and the parameters. We begin by examining a system know for exhibiting chaotic dynamics and then move on to a spatially extended system. First, we study the effect of low-pass band filters on the dynamics of a non-isothermal autocatalator by selecting Fourier coefficients for the modes in the pass band according to a uniform distribution. Numerical simulations over many realizations of feedback are compared to theoretical predictions for the feedback size as a function of the parameter. We find that the variance in the feedback is non-zero only nearby to and within chaotic regimes in the parameter space. We numerically calculate the probability density for the parameter showing that the system adapts to the edge of chaos. We attempt to expand on this work to a spatially extended system. Although an analytical description of the natural dynamics for video feedback is beyond the scope of this work, we model video feedback in one-dimension and examine the effects of spatially averaging feedback mechanism onto a system parameter. While the unfiltered dynamics approach a fixed point for the entire parameter range, we also identify parameter ranges where the filtered system adapts to non-linear oscillations as well as fixed points.
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