The 2015 AMMCS-CAIMS Congress
Interdisciplinary AMMCS Conference SeriesWaterloo, Ontario, Canada | June 7-12, 2015
AMMCS-CAIMS 2015 Plenary Talk
Noise Impact on Finite Dimensional Dynamical Systems
Yingfei Yi (University of Alberta)
Dynamical systems are often subjected to noise perturbations either from external sources or from their own intrinsic uncertainties. While it is well believed that noises can have dramatic effects on the stability of a deterministic system at both local and global levels, mechanisms behind noise surviving or robust dynamics have not been well understood especially from distribution perspectives. This talk attempts to outline a mathematical theory for making a fundamental understanding of these mechanisms in white noise perturbed systems of ordinary differential equations, based on the study of stationary measures of the corresponding Fokker-Planck equations. New existence and non-existence results of stationary measures will be presented by relaxing the notion of Lyapunov functions. Limiting behaviors of stationary measures as noises vanish will be discussed in connection to important issues such as stochastic stability and bifurcations.
Yingfei Yi obtained his B.S. degree in classical mechanics from Jilin University in 1984 and his Ph.D degree in applied mathematics from the University of Southern California in 1990. His professional career started at Georgia Institute of Technology, first as a Postdoctoral Fellow at the Center for Dynamical Systems and Nonlinear Studies from 1990-1992, then at the School of Mathematics as an Assistant Professor from 1992-1997, an Associate Professor from 1997-2000, and a Professor from 2000. He jointed the Department of Mathematical and Statistical Sciences, the University of Alberta in 2014 as a Killam Memorial Chair in Dynamical Systems. He received a Rosenbaum Fellowship from the University of Cambridge in 1995, a University Research Fellowship from Jilin University in 1998, an Outstanding Young Scientist Award from NSFC in 2004, a Changjiang Scholarship from MoE, China and Li Ka Shing Foundation in 2008, and a Chinese National Qianren Research Chair Professorship in 2009 from MoE, China. He is a Co-editor in Chief for the Journal of Dynamics and Differential Equations, a handling editor for the Journal of Differential Equations, an editor for the Proceedings of the American Mathematical Society, an editor for the SIAM DSweb Magazine, and he is also an associate editor or a member of editorial board of three other professional journals. His research interests lie in dynamical systems and qualitative theory of differential equations.