{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/31343"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/31343","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Adaptation to the Edge of Chaos and Critical Scaling in Self-adjusting Dynamical Systems","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Melby, Paul Christian"],"institution":null,"degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Physics","degree_department":null,"school":null,"contributors":["Hubler, Alfred W."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2012,"date_issued":"2012-06-05T18:35:39Z","date_published":"2012-06-05T18:35:39Z","updated_at":"2026-07-22T22:25:30Z","subjects":["dynamical systems","self-adjusting systems","edge of chaos"],"languages":["en"],"rights":["©2002 Melby"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["4591801"],"render_values":[{"text":"4591801","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/31343","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Hubler, Alfred W."]},{"key":"dc:creator","label":"Author","values":["Melby, Paul Christian"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2012-06-05T18:35:39Z","10000-01-01","2002"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation / Thesis","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."]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["dynamical systems","self-adjusting systems","edge of chaos"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["©2002 Melby"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/31343","4591801"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["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.","Submitted by William Weathers (weathrs2@illinois.edu) on 2012-06-05T18:35:39Z No. of bitstreams: 1 2002_melby.pdf: 2407807 bytes, checksum: d424310966737b86dee80c7670c0f4a1 (MD5)","Made available in DSpace on 2012-06-05T18:35:39Z (GMT). No. of bitstreams: 1 2002_melby.pdf: 2407807 bytes, checksum: d424310966737b86dee80c7670c0f4a1 (MD5) Previous issue date: 2002","Restriction data tranferred 2014-07-01T11:10:50-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: Thesis","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by William Weathers (weathrs2@illinois.edu) on 2012-06-05T18:35:39Z Item is restricted indefinitely.","Thesis","U of I Only"]},{"key":"dc:title","label":"Title","values":["Adaptation to the Edge of Chaos and Critical Scaling in Self-adjusting Dynamical Systems"]}]}],"canonical_facts":{"dc:contributor":["Hubler, Alfred W."],"dc:creator":["Melby, Paul Christian"],"dc:date":["2012-06-05T18:35:39Z","10000-01-01","2002"],"dc:description":["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.","Submitted by William Weathers (weathrs2@illinois.edu) on 2012-06-05T18:35:39Z No. of bitstreams: 1 2002_melby.pdf: 2407807 bytes, checksum: d424310966737b86dee80c7670c0f4a1 (MD5)","Made available in DSpace on 2012-06-05T18:35:39Z (GMT). No. of bitstreams: 1 2002_melby.pdf: 2407807 bytes, checksum: d424310966737b86dee80c7670c0f4a1 (MD5) Previous issue date: 2002","Restriction data tranferred 2014-07-01T11:10:50-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: Thesis","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by William Weathers (weathrs2@illinois.edu) on 2012-06-05T18:35:39Z Item is restricted indefinitely.","Thesis","U of I Only"],"dc:identifier":["http://hdl.handle.net/2142/31343","4591801"],"dc:language":["en"],"dc:rights":["©2002 Melby"],"dc:subject":["dynamical systems","self-adjusting systems","edge of chaos"],"dc:title":["Adaptation to the Edge of Chaos and Critical Scaling in Self-adjusting Dynamical Systems"],"dc:type":["Dissertation / Thesis","text"],"thesis:degree_discipline":["Physics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."]},"updated_at":"2026-07-22T22:25:30Z"}