System identification near a hopf bifurcation via the noise-induced dynamics in the fixed-point regime

Abstract

First and foremost, I would like to express my deepest appreciation to my supervisor, Prof. Larry K.B. Li, for his invaluable guidance and support. I have been very fortunate to have an advisor who patiently taught me how to develop ideas and formulate arguments in a scientific manner. His encouragement has been the greatest contributor to the completion of this thesis.I would also like to extend my sincere gratitude to Prof. Vikrant Gupta at SUSTech for his constructive advice throughout my study. His insightful comments steered me in the right direction. I am also grateful to Prof. Kyutae Kim and his team at KAIST for their kind help and cooperation at the final stage of my research.I have great pleasure in acknowledging Mr. Yuanhang Zhu at Brown University and Dr. Yu Guan at HKUST who carried out all the experiments in Chapters 2 and 3, respectively. This thesis would not have been possible without their help.Most importantly, I am thankful to my family for their incredible support and understanding. I am grateful to my two sets of parents, who have given me wise counsel. I thank my daughter, Yerin, for her ability to make me smile. Above all, I heartily thank my wife Aram for her encouragement and inspiration throughout my study.Last but not least, I would like to thank the Research Grants Council of Hong Kong and LG CNS for their financial and academic support. v

An Optimized Dynamic Mode Decomposition Model Robust to Multiplicative Noise

“…The combustor is spatially divided into 500 equal-length segments. We set the parameters of (5.5) as follows: Ma = 0.005, x f = 0.25, τ = 0.16, k Q = 0.0035, and γ = 1.4, following previous practices [31,32]. By numerically solving this time-marching problem, we obtain a data matrix X whose rows represent the spatial distribution of p ′ and columns represent the time.…”