Adaptation to the Edge of Chaos and Critical Scaling in Self-adjusting Dynamical Systems
Melby, Paul Christian
This item is only available for download by members of the University of Illinois community. Students, faculty, and staff at the U of I may log in with your NetID and password to view the item. If you are trying to access an Illinois-restricted dissertation or thesis, you can request a copy through your library's Inter-Library Loan office or purchase a copy directly from ProQuest.
Permalink
https://hdl.handle.net/2142/31343
Description
Title
Adaptation to the Edge of Chaos and Critical Scaling in Self-adjusting Dynamical Systems
Author(s)
Melby, Paul Christian
Issue Date
2002
Doctoral Committee Chair(s)
Hubler, Alfred W.
Department of Study
Physics
Discipline
Physics
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
dynamical systems
self-adjusting systems
edge of chaos
Language
en
Abstract
We present a mechanism for adaptation in dynamical systems. Systems
which have this mechanism are called called self-adjusting systems. The
control parameters in a self-adjusting system are slowly varying, rather than
constant. The dynamics of the control parameters are governed by a lowpass
filtered feedback from the dynamical variables. We apply this model to
several systems, numerically, analytically, and experimentally, and examine
the behavior of the control parameters. We observe a high probability of
finding the parameter at the boundary between periodicity and chaos. We
therefore find that self-adjusting systems adapt to the edge of chaos. In
addition, we find that noise in the system drives the parameter away from
the edge of chaos on very long timescales so that chaos is suppressed in the
system. We show that, with the presence of noise, the parameter can re-enter
the chaotic regime. This is called a chaotic outbreak in the system and we
find that the distribution of outbreaks is a power-law with the duration of the
outbreak. We then study the robustness of adaptation to the edge of chaos
by examining the effect of a control force being applied to the parameter.
We find the behavior to be very robust, except for very large control forces.
Finally, we look at systems of coupled maps and show that adaptation to the
edge of chaos occurs in systems of higher dimensions, as well.
Use this login method if you
don't
have an
@illinois.edu
email address.
(Oops, I do have one)
IDEALS migrated to a new platform on June 23, 2022. If you created
your account prior to this date, you will have to reset your password
using the forgot-password link below.
