A Quantification of Long Transient Dynamics
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Authors
Liu, Ankai
Date
Type
thesis
Language
eng
Keyword
Differential equations , Transient dynamics , Transient centers , Transient centres
Alternative Title
Abstract
We present a systematic study of transient dynamics starting with a technical definition of transient points which are initial data of an autonomous system of ordinary differential equations that can lead to “long transient dynamics.” We then define transient centers, which are points in the state space that cause long transient behaviors, and reachable transient centers, which are transient centers that can be reached from initializations that do not need to be nearby. These points give rise to dynamics where a prescribed observable changes arbitrarily slowly for arbitrarily long time durations. We demonstrate the many interesting properties of transient centers, including how it easily translates from point to point: if an initial point is a transient center then so are all the points in its entire trajectory forward and backward in time, as well as any limit points. Finally, we also explore how these ideas are related to established concepts in dynamical systems such as slow-fast systems, turning points and Lyapunov regularity.
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Queen's University's Thesis/Dissertation Non-Exclusive License for Deposit to QSpace and Library and Archives Canada
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This publication is made available by the authority of the copyright owner solely for the purpose of private study and research and may not be copied or reproduced except as permitted by the copyright laws without written authority from the copyright owner.
Attribution-NonCommercial 3.0 United States
ProQuest PhD and Master's Theses International Dissemination Agreement
Intellectual Property Guidelines at Queen's University
Copying and Preserving Your Thesis
This publication is made available by the authority of the copyright owner solely for the purpose of private study and research and may not be copied or reproduced except as permitted by the copyright laws without written authority from the copyright owner.
Attribution-NonCommercial 3.0 United States