报告人：Michael Small（司马乐）教授 （澳大利亚Western Australia大学），澳大利亚Future Fellow（澳大利亚“千人计划”）
Title: Constructing a dynamical model from limited data --- a granular media case-study
Abstract: Inferring deterministic dynamical behavior from observed data is a long standing problem with a wide range of useful applications. The prototypical example involves an experimentally observed time series from some low-dimensional system and subsequent attempts to infer as much information as possible concerning the underlying deterministic dynamics. While there are some very well established techniques to achieve parts of this goal, the methods are not without problems. I will describe some recent additions to this collection of techniques, primarily inspired by the field of complex systems and complex networks, and discuss how best to avoid the most obvious pitfalls. As an example, I will present results for the case of large strain behavior of a granular material under biaxial compression. In the approximately steady-state regime we find that this system exhibits behavior consistent with a (hyper-) chaotic dynamical system.
Michael Small is an Australian Research Council Future Fellow and Winthrop Professor of Applied Mathematics in the School of Mathematics and Statistics at The University of Western Australia (UWA). His research interests are complex systems, nonlinear dynamics and chaos, and nonlinear time series analysis. Prof. Smalls work focusses on the application of mathematical methods to a variety of problems in the real world: social and technological networks, neurodynamics, modelling of physical systems, biomedical signal processing and financial markets are a few examples. He is interested in how the structure of a complex network affects the dynamical behaviour of its components and is developing techniques to characterise and quantify regularity and atypical features in complex networks. He is currently working on applications of complex networks and dynamical complex networks to problems in systems biology, collective animal motion and disease transmission.
Prior to joining UWA in 2012, Prof. Small was with the Department of Electronic and Information Engineering at The Hong Kong Polytechnic University. He is a Senior member of the IEEE and the Australian Mathematics Society, and on the editorial board of several international journals - including the International Journal of Bifurcations and Chaos. Prof. Small has published well over 130 journal articles and authored or co-authored four books.