Rate-induced critical transitions

Xie, Chun

Rate-induced critical transitions

dc.availability.bitstream	openaccess
dc.contributor.advisor	Wieczorek, Sebastian	en
dc.contributor.author	Xie, Chun
dc.contributor.funder	H2020 Marie Skłodowska-Curie Actions	en
dc.date.accessioned	2020-05-20T09:00:48Z
dc.date.available	2020-05-20T09:00:48Z
dc.date.issued	2020-04
dc.date.submitted	2020-04
dc.description.abstract	This thesis focuses on rate-induced critical transitions or tipping points (R-tipping points), where the system undergoes a critical transition if the time-varying external conditions vary faster than some critical rate. Such a critical transition is usually a sudden and unexpected change of the system state. The change can be either irreversible: a permanent tipping point with no return to the original state, or reversible: a temporary tipping point with self-recovery back to the original state, both of which may cause significant consequences in applications. Indeed, R-tipping is an ubiquitous nonlinear phenomenon in nature that remains largely unexplored by the scientists. From a mathematical viewpoint, it is a genuine nonautonomous instability that cannot be explained by the classical (autonomous) bifurcation theory and requires an alternative approach. The first part of the thesis focuses on a mathematical framework for R-tipping in systems of nonautonomous differential equations, where the nonautonomous terms representing time-varying external conditions decay asymptotically. In particular, special compactification techniques for asymptotically autonomous systems are developed to simplify analysis of R-tipping. In the second part of the thesis, the main concepts of edge states and thresholds are introduced to define the R-tipping phenomenon. Then, simple testable criteria for the occurrence of reversible and irreversible R-tipping in arbitrary dimension are given. This part extends the previous results on irreversible R-tipping in one dimension. The third part of the thesis identifies canonical examples of R-tipping based on the system dimension, timescales and the threshold type. These examples are relatively simple low-dimensional nonlinear systems that capture different R-tipping mechanisms. R-tipping analysis of canonical examples, which is underpinned by the compactification framework developed in the second part, reveals intricate R-tipping diagrams with multiple critical rates and transitions between different types of R-tipping.	en
dc.description.status	Not peer reviewed	en
dc.description.version	Accepted Version	en
dc.format.mimetype	application/pdf	en
dc.identifier.citation	Xie, C. 2020. Rate-induced critical transitions. PhD Thesis, University College Cork.	en
dc.identifier.endpage	158	en
dc.identifier.uri	https://hdl.handle.net/10468/9990
dc.language.iso	en	en
dc.publisher	University College Cork	en
dc.relation.project	info:eu-repo/grantAgreement/EC/H2020::MSCA-ITN-ETN/643073/EU/Critical Transitions in Complex Systems/CRITICS	en
dc.rights	© 2020, Chun Xie.	en
dc.rights.uri	https://creativecommons.org/licenses/by-nc-nd/4.0/	en
dc.subject	Asymptotically autonomous differential equations	en
dc.subject	Compactification	en
dc.subject	Nonautonomous dynamical systems	en
dc.subject	Rate-induced tipping	en
dc.subject	Threshold and edge state	en
dc.subject	Connecting orbits and canards	en
dc.title	Rate-induced critical transitions	en
dc.type	Doctoral thesis	en
dc.type.qualificationlevel	Doctoral	en
dc.type.qualificationname	PhD - Doctor of Philosophy	en