{"id":{"repo_id":"cork","oai_identifier":"oai:cora.ucc.ie:10468/15016"},"canonical_url":"https://search.dev.ndltd.org/etd/cork/oai:cora.ucc.ie:10468/15016","repository":{"repo_id":"cork","name":"University College Cork","base_url":"https://cora.ucc.ie/server/oai/request"},"display":{"title":"Rate-induced tipping to metastable Zombie fires","abstract":"Surface wildfires are generally believed to be the cause of so-called Zombie fires observed in peatlands, that disappear from the surface, smoulder underground during the winter, and ''come back to life" in the spring. Here, we propose rate-induced tipping (R-tipping) to a subsurface hot metastable state in bioactive peat soils as a main cause of Zombie fires. Our hypothesis is based on a conceptual soil-carbon model subjected to realistic changes in weather and climate patterns, including global warming scenarios and summer heatwaves. Mathematically speaking, R-tipping to the hot metastable state is a nonautonomous instability, due to crossing an elusive quasithreshold, in a multiple-timescale dynamical system. The instability is {\\em reversible}, in the sense that the system eventually returns to its base state. To explain this instability, we provide a framework that combines a special compactification technique with concepts from geometric singular perturbation theory. This framework allows us to reduce a reversible R-tipping problem due to crossing a quasithreshold to a heteroclinic orbit problem in a singular limit. Thus, we identify generic cases of such R-tipping via: (i) unfolding of a codimension-two heteroclinic folded saddle-node type-I singularity for global warming, and (ii) analysis of a codimension-one saddle-to-saddle hetroclinic orbit for summer heatwaves, which in turn reveal new types of excitability quasithresholds.","abstract_html":"Surface wildfires are generally believed to be the cause of so-called Zombie fires observed in peatlands, that disappear from the surface, smoulder underground during the winter, and ''come back to life" in the spring. Here, we propose rate-induced tipping (R-tipping) to a subsurface hot metastable state in bioactive peat soils as a main cause of Zombie fires. Our hypothesis is based on a conceptual soil-carbon model subjected to realistic changes in weather and climate patterns, including global warming scenarios and summer heatwaves. Mathematically speaking, R-tipping to the hot metastable state is a nonautonomous instability, due to crossing an elusive quasithreshold, in a multiple-timescale dynamical system. The instability is {\\em reversible}, in the sense that the system eventually returns to its base state. To explain this instability, we provide a framework that combines a special compactification technique with concepts from geometric singular perturbation theory. This framework allows us to reduce a reversible R-tipping problem due to crossing a quasithreshold to a heteroclinic orbit problem in a singular limit. Thus, we identify generic cases of such R-tipping via: (i) unfolding of a codimension-two heteroclinic folded saddle-node type-I singularity for global warming, and (ii) analysis of a codimension-one saddle-to-saddle hetroclinic orbit for summer heatwaves, which in turn reveal new types of excitability quasithresholds.","abstract_has_math":false,"creators":["O'Sullivan, Eoin"],"institution":"University College Cork","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Mulchrone, Kieran F.","Wieczorek, Sebastian"],"committee_chairs":[],"committee_members":[],"year":2023,"date_issued":"2023","date_published":"2023","updated_at":"2026-07-24T01:48:31Z","subjects":["Applied mathematics","Zombie fires","Rate-induced tipping","Canards","Geometric singular perturbation theory"],"languages":["en"],"rights":["© 2023, Eoin O'Sullivan."],"rights_urls":["https://creativecommons.org/licenses/by/4.0/"],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/10468/15016","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Mulchrone, Kieran F.","Wieczorek, Sebastian"]},{"key":"dc:creator","label":"Author","values":["O'Sullivan, Eoin"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2023-09-20T14:52:20Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2023-09-20T14:52:20Z"]},{"key":"dc:date.issued","label":"Date","values":["2023"]},{"key":"dc:publisher","label":"Institution","values":["University College Cork"]},{"key":"dc:type","label":"Dc Type","values":["Doctoral thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["Doctoral"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["PhD - Doctor of Philosophy"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Applied mathematics","Zombie fires","Rate-induced tipping","Canards","Geometric singular perturbation theory"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["© 2023, Eoin O'Sullivan."]},{"key":"dc:rights.uri","label":"Rights URI","values":["https://creativecommons.org/licenses/by/4.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/10468/15016"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Surface wildfires are generally believed to be the cause of so-called Zombie fires observed in peatlands, that disappear from the surface, smoulder underground during the winter, and ''come back to life" in the spring. Here, we propose rate-induced tipping (R-tipping) to a subsurface hot metastable state in bioactive peat soils as a main cause of Zombie fires. Our hypothesis is based on a conceptual soil-carbon model subjected to realistic changes in weather and climate patterns, including global warming scenarios and summer heatwaves. Mathematically speaking, R-tipping to the hot metastable state is a nonautonomous instability, due to crossing an elusive quasithreshold, in a multiple-timescale dynamical system. The instability is {\\em reversible}, in the sense that the system eventually returns to its base state. To explain this instability, we provide a framework that combines a special compactification technique with concepts from geometric singular perturbation theory. This framework allows us to reduce a reversible R-tipping problem due to crossing a quasithreshold to a heteroclinic orbit problem in a singular limit. Thus, we identify generic cases of such R-tipping via: (i) unfolding of a codimension-two heteroclinic folded saddle-node type-I singularity for global warming, and (ii) analysis of a codimension-one saddle-to-saddle hetroclinic orbit for summer heatwaves, which in turn reveal new types of excitability quasithresholds."]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Rate-induced tipping to metastable Zombie fires"]}]}],"canonical_facts":{"dc:contributor.advisor":["Mulchrone, Kieran F.","Wieczorek, Sebastian"],"dc:creator":["O'Sullivan, Eoin"],"dc:date.accessioned":["2023-09-20T14:52:20Z"],"dc:date.available":["2023-09-20T14:52:20Z"],"dc:date.issued":["2023"],"dc:description.abstract":["Surface wildfires are generally believed to be the cause of so-called Zombie fires observed in peatlands, that disappear from the surface, smoulder underground during the winter, and ''come back to life" in the spring. Here, we propose rate-induced tipping (R-tipping) to a subsurface hot metastable state in bioactive peat soils as a main cause of Zombie fires. Our hypothesis is based on a conceptual soil-carbon model subjected to realistic changes in weather and climate patterns, including global warming scenarios and summer heatwaves. Mathematically speaking, R-tipping to the hot metastable state is a nonautonomous instability, due to crossing an elusive quasithreshold, in a multiple-timescale dynamical system. The instability is {\\em reversible}, in the sense that the system eventually returns to its base state. To explain this instability, we provide a framework that combines a special compactification technique with concepts from geometric singular perturbation theory. This framework allows us to reduce a reversible R-tipping problem due to crossing a quasithreshold to a heteroclinic orbit problem in a singular limit. Thus, we identify generic cases of such R-tipping via: (i) unfolding of a codimension-two heteroclinic folded saddle-node type-I singularity for global warming, and (ii) analysis of a codimension-one saddle-to-saddle hetroclinic orbit for summer heatwaves, which in turn reveal new types of excitability quasithresholds."],"dc:format.mimetype":["application/pdf"],"dc:identifier.uri":["https://hdl.handle.net/10468/15016"],"dc:language.iso":["en"],"dc:publisher":["University College Cork"],"dc:rights":["© 2023, Eoin O'Sullivan."],"dc:rights.uri":["https://creativecommons.org/licenses/by/4.0/"],"dc:subject":["Applied mathematics","Zombie fires","Rate-induced tipping","Canards","Geometric singular perturbation theory"],"dc:title":["Rate-induced tipping to metastable Zombie fires"],"dc:type":["Doctoral thesis"],"dc:type.qualificationlevel":["Doctoral"],"dc:type.qualificationname":["PhD - Doctor of Philosophy"]},"updated_at":"2026-07-24T01:48:31Z"}