{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/80624"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/80624","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Migration Towards Periodicity in Systems With Feedback","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Wotherspoon, Timothy David"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Physics","degree_department":null,"school":null,"contributors":["Karin Dahmen"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-09-25T20:03:20Z","date_published":"2015-09-25T20:03:20Z","updated_at":"2026-07-22T22:26:14Z","subjects":["Physics, Theory"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(MiAaPQ)AAI3395541"],"render_values":[{"text":"(MiAaPQ)AAI3395541","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/80624","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Karin Dahmen"]},{"key":"dc:creator","label":"Author","values":["Wotherspoon, Timothy David"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-09-25T20:03:20Z","10000-01-01","2009"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Physics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Physics, Theory"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/80624","(MiAaPQ)AAI3395541"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["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.","Made available in DSpace on 2015-09-25T20:03:20Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3395541.pdf: 705563 bytes, checksum: eeb006225f77285968283ff2a455ff42 (MD5) Previous issue date: 2009","Embargo set by: Seth Robbins for item 81906 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","54 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2009."]},{"key":"dc:title","label":"Title","values":["Migration Towards Periodicity in Systems With Feedback"]}]}],"canonical_facts":{"dc:contributor":["Karin Dahmen"],"dc:creator":["Wotherspoon, Timothy David"],"dc:date":["2015-09-25T20:03:20Z","10000-01-01","2009"],"dc:description":["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.","Made available in DSpace on 2015-09-25T20:03:20Z (GMT). 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