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Title: Non-autonomous random dynamical systems : stochastic approximation and rate-induced tipping
Author: Hartl, Michael
ISNI:       0000 0004 8499 5067
Awarding Body: Imperial College London
Current Institution: Imperial College London
Date of Award: 2019
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In this thesis we extend the foundational theory behind and areas of application of non-autonomous random dynamical systems beyond the current state of the art. We generalize results from autonomous random dynamical systems theory to a non-autonomous realm. We use this framework to study stochastic approximations from a different point of view. In particular we apply it to study noise induced transitions between equilibrium points and prove a bifurcation result. Then we turn our attention to parameter shift systems with bounded additive noise. We extend the framework of rate induced tipping in deterministic parameter shifts for this case and introduce tipping probabilities. Finally we perform a case study by developing and applying a numerical method for calculating tipping probabilities and examining the results thereof.
Supervisor: van Strien, Sebastian ; Rasmussen, Martin Sponsor: European Commission
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral